source : mathsisfun.com
Quadratic Equation Solver
We can help you solve an equation of the form “ax2 + bx + c = 0” Just enter the
values of a, b and c below:
Is it Quadratic?
Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.
The name comes from “quad” meaning square, as the variable is squared (in other words x2).
These are all quadratic equations in disguise:
In standard form
a, b and c
x2 = 3x -1
x2 – 3x + 1 = 0
a=1, b=-3, c=1
2(x2 – 2x) = 5
2×2 – 4x – 5 = 0
a=2, b=-4, c=-5
x(x-1) = 3
x2 – x – 3 = 0
a=1, b=-1, c=-3
5 + 1/x – 1/x2 = 0
5×2 + x – 1 = 0
a=5, b=1, c=-1
How Does this Work?
The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:
The “±” means we need to do a plus AND a minus, so there are normally TWO solutions !
The blue part (b2 – 4ac) is called the “discriminant”, because it can “discriminate” between the possible types of answer:
when it is positive, we get two real solutions,
when it is zero we get just ONE solution,
when it is negative we get complex solutions.
Learn more at Quadratic Equations
Note: you can still access the old version here.
Program to find number of solutions in Quadratic Equation – Solution: To check whether the equation has a solution or not, quadratic formula for discriminant is used. Check whether one root of the Quadratic Equation is twice of other or not.Solve quadratic equations using a quadratic formula calculator. Calculator solution will show work for real and complex roots. Uses the quadratic formula to solve a second-order polynomial equation or quadratic equation. Shows work by example of the entered equation to find the real or complex root…Algebra Quadratic Equations and Functions Solutions Using the Discriminant. The discriminant is the portion #(b^2-4ac)# if it is negative then the roots include a term which is the square root of a negative number; since there are no Real numbers whose square root is negative, when the…
Quadratic Formula Calculator – A quadratic equation is of the form of.. where a, b and c are coefficient then, the solution is given by On comparing the given equation with equation  we have; a = -1 , b = 0 and c =98.Reviews how to solve quadratics by using the Quadratic Formula. But the Quadratic Formula will always spit out an answer, whether or not the quadratic expression was factorable. Let's try that first problem from the previous page again, but this time we'll use the Quadratic Formula instead of the…Quadratic Equation Solver. We can help you solve an equation of the form "ax2 + bx + c = 0" Just enter the values of a, b and c below How Does this Work? The solution(s) to a quadratic equation can be calculated using the Quadratic Formula: The "±" means we need to do a plus AND a minus…
How do you use the discriminant to find the number of real solutions… – What are the solutions of the quadratic equation? 4 years ago. 2nd equation: y-x = 2 would be written as y= 2+x Substituting this interior the 1st equation, 2 + x = x^2 + 5x -3 bringing all like words jointly, 2 + 3 = x^2 + 5x – x 5 = x^2 + 4x Now, to locate the cost of x , equate the polynomial to 0. X^2…Applications of Quadratic Equations. Related Topics: More Lessons for Basic Algebra Math Worksheets. Scroll down the page for more examples and solutions for quadratic equations in vertex form. The Vertex and Axis of Symmetry In a parabola, the vertex is the highest or lowest point…The solutions to the quadratic equation x2 – 11x + 22 = 0 are x = 3 and x = 6. What is the base of the numbers? Strange question!
Ex 4.3 class 10| Quadratic formula | Quadratic Equations [Q2 All parts] – Unknown: Welcome to R&H Academy
Till yet, we have known two methods to solve a quadratic
equation first is splitting the middle term. Second is
completing the square method. Today, we will learn third
method, which is quadratic formula, quadratic formula is x equals to
minus b plus minus root d by two A, B is the coefficient of x,
A is the coefficient of x sq whereas, D is b square minus 4ac. D stands for
discriminant. And that's all you need to know to solve question
number two, of Exercise 4.2 So,let's start. What is a? a is
the coefficient of x square, B is coefficient of x that is
minus seven, C is constant. Now, find out the D. D is equal to b square minus
4AC, substitute the values B is minus seven minus seven whole
square minus four, multiply a, multiply three minus seven
square is 49. Minus four multiply two multiply three is 24. And 49 minus 24 is 25. Now, use
the formula x is equals to minus b plus minus root d by 2a.
Substitute the values, B is minus seven, plus minus, under root or square root of
twenty five by two multiply two. Let's simplify. x is equal to minus of minus seven is plus
seven, plus minus square root of 25 is five divided by two multiply two is four. So x equals to seven, plus
four minus five is equal to four. x is equal to seven plus
five divided by four. x is equals to seven minus 5 divided
by four, seven plus five is 12. 12 by four is three, seven minus
five is two by four and two by four is one by three and one by
two are the values of x. Step one is to write the value of a,
which is coefficient of x square. B is the cofficient of
x, that is one, C is constant, that is minus four. Step two is
to find the value of D or discriminant. substitute these values b square is one square, minus
four, multiply a that is two. Multiply, c that is minus four. One square is one, minus four multiply two multiply
minus four is plus 32. And one plus 32 is 33. Use the
formula x is equals to minus b plus minus root d by two A minus B is minus one, plus minus root B is root 33
divided by two, multiply a, that is four. So x is equals to minus
one plus root 33 divided by two multiply two is four. Another is
x equals to minus one minus root 33 divided by four. These are
the roots of given equation; roots or solutions or the zeroes
of the given quadratic equation. Let's move to part three A, B, and C. A is coefficient of x square,
b is coefficient of x, C is constant. Find D, D is equals to b square minus four AC. B is four root
three whole square. minus four, multiply a multiply C, four root three square is Four square, multiply root three
square, four square is 16. And root three square is 3. 16
Multiply three is 48. 48 minus four, 4 x 4 = 16. 16 into three
is 48. And 48 minus 48 is zero, use the quadratic formula, x is
equals to minus b plus minus root d by two A minus B is minus
four root three, plus minus b is zero, square root of zero,
divided by two, multiply eight, that is four minus four Three plus minus square root of zero is zero divided by eight. So x is minus 4 root 3 by eight, plus zero will give minus four root three by x is
equals to minus four root three, minus zero by 8. minus four root
three minus zero is minus four, three, divided by eight. Step one is to write the values of A, B
and C. A is two B is one, C is four, D is equal to b square minus 4AC. b square is one square
minus four, multiply a, multiply c, one square is one minus four multiply two multiply four is 32. And one
minus 32 is minus 31. Since D is less than zero, real
roots of the given quadratic equation do not exist. So our D
should always be greater than or equal to zero. For roots to
exist, else real roots do not exist. Thank you so much for
Can You Solve The Viral 9 = 72 Puzzle? The Correct Answer Explained – Hey this is Presh Talwalkar.
has been shared millions of times on Facebook and Twitter with the claim that
99% failed to solve it, and that only a genius could find the correct answer. In
this video I'm going to explain what many people believe to be the correct
answer. Can you figure it out? Give this problem a try. And when you're ready, keep watching the video for the solution. So most people believe the correct answer is 6. The pattern is to take the number on the left hand side of the equation and multiply it by 1 less than itself. For example the first line would read 9
times 8 which equals 72. The next line would be 8 times 7 which equals 56. We then have 7 times 6 which equals 42. 6 times 5 which equals 30. 5 times 4 which equals 20. And finally we would have 3 times 2 which equals 6. But not everyone believes 6 is the correct answer. Some people argue the correct answer is 12. They identify a pattern of decreasing subtraction in the number on the right hand side. So let's see how this pattern works. We start out with 9 equals 72. To get to the next line we subtract by 16 to get to 56. So that is why 8 equals 56. Now how do we get to the next line?
Rather than subtracting by 16 they would say you should decrease the amount
you're subtracting by to be 14. So then we have 56 minus 14 equals 42. This gives us the next line of 7 equals 42. We now subtract by 2 less so we have 42 minus
12 which equals 30. And that gets us to the next line. We
then subtract by two less again so we have 30 minus 10 which equals 20. So we
have 5 equals 20 and then we want to subtract by 2 less which will be 8. And
that will be 20 minus 8 which equals 12. And that's why they argue the answer is 3 equals 12. But hold on! There's a third group of people who say the answer is neither 6 nor 12 but actually that the answer is 9. Their method is looking at a pattern of decreasing multiplication. So this is very much like the answer being 6. You multiply a number by one less than itself. The difference in this method is now
they say look at the numbers you're multiplying by. This is a sequence of
numbers. We have 8, 7, 6, 5, and 4. So this group of people argues that
if you decrease this you would get the next line, which means you should
multiply the next line by 3. So they would say the answer is 3 times
3 which equals 9. So now let's recap the three different answers. Some people say the answer is 6; other people say the answer is 12; and even
other people say the answer is 9. Now it's a common question which of these answers is correct. Is there a more correct answer than any of the others? Well from the information we're given in the puzzle we can't definitively say. But what we can do is we can ask: is any of these answers is justifiable under the
patterns of the given methods? And by that standard, the answer of 6 is
justifiable by the two other methods. We can actually reconcile this to show that 6 is a very reasonable answer. How can we do that? Let's start out with the logic of the decreasing subtraction. So here's the information of the pattern.
Each time you're subtracting by 2 less than before. So now the question is: is there, or are there any other patterns, in this? Well
what you can do is focus on the first number in each line. We have a sequence
here. We have 9, 8, 7, 6, and 5. By this logic–that we should have a
sequence–we should then have a sequence that the next line be 1 less than 5.
So the next line should be 4. And by the logic of decreasing subtraction we would then have 4 equals 12. So then how do we figure out what the next line is? How do we get to what 3 equals? Well we look at the numbers we're
subtracting by. If we have this logic of decreasing subtraction we should subtract by 2 less than 8 so that means the next line would have 12 minus
6. And that would give us the answer on the right-hand side of the next line
which equals 6. So if we decrease 4 we then have the next line being 3 and then
we have the answer of 6 by this decreasing subtraction method. So once
again we figured out that 3 equals 6 and the answer is 6 by the very same
decreasing subtraction method. The only thing we had to do is we had to add the missing line of 4 equals 12. We can use the same kind of logic for the
decreasing multiplication method. Here's the information from the pattern which they argue about the decreasing multiplication method. So we're supposed to be looking for a logic to this–these numbers. But what we can do–is–we can
look at the first number in every single line. We have a sequence here of numbers
9, 8, 7, 6, and 5. So logic would suggest the next line should start out with 4. We then look at the numbers that we are multiplying by and that's another sequence 8, 7, 6, 5, & 4. So logic would suggest the next line should be multiplied by 3. So the next line should be 4 multiplied by 3 equals 12. If we continue this pattern the first number will be one less and the second
number will be one less so the next line would be 3 times 2. And once again
3 times 2 equals 6. So we again have the answer being equal to 6. This is even true under the decreasing multiplication method as long as we include the missing line of 4 times 3 equals 12. So to recap: it doesn't matter which method we're using. We're always going to get to the answer that 3 equals 6. And in fact we would have 4 equals 12 in each of these methods too. So this logic would suggest that the correct answer to this puzzle is that 3 equals 6. What do you think? Thanks for watching this video! Please subscribe to my channel, I make videos on math and game theory. You can catch on my blog MindYourDecisions which you can follow on Facebook Google+ and Patreon. You can catch me on social media @preshtalwalkar And if you like this video please check out my books! There are links in the video description. .
5.7 Algebra 2 – .