# According To The Rational Root Theorem, Which Statement About F(x) = 12x^3 – 5x^2 + 6x + 9 Is True?

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## According to the Rational Root Theorem, which statement about f(x) = 12x^3 – 5x^2 + 6x + 9 is true?

y=12x^3-5x^2+6x+9

Any rational root will be of the form

+-(factor of 9)/(factor of 12)

So we have +-(1,3,9)/(1,2,3,4,6,12) as possibilities.

Think of it this way

Let it be factored as (ax+b)(cx+d)(ex+f)

So a*c*e=12 and b*d*f=9

If this is factored form, (-b/a),(-d/c),(-f/e) will be roots.

This proves that rational roots will be

+-(factor of 9)/(factor of 12)

None of these forms will be a root and therefore the roots of this particular equation are irrational. This can be verified by synthetic division. They are -.6387559, .5277113+-.9464028i

Rational Root Theorem | Brilliant Math & Science Wiki – These are some of the associated theorems that closely follow the rational root theorem. The first one is the integer root theorem. If f (x) f(x) f (x) is a monic polynomial (leading coefficient of 1), then the rational roots of f (x) f(x) f (x) must be integers.Free Rational Roots Calculator – find roots of polynomials using the rational roots theorem step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy.According to the Rational Root Theorem, which statement about f(x) = 12x^3- 5x^2 + 6x + 9 is true? A: Any rational root of f(x) is a multiple of 12 divided by a multiple of 9. B: Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.

Rational Roots Calculator – Symbolab – According to the Rational Root Theorem, which statement about f(x) = 12x^3 – 5x^2 + 6x + 9 is true? A) Any rational root of f(x) is a multiple of 12 divided by a multiple of 9. B) Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.According to the Rational Root Theorem, which statement about f(x) = 66×4 – 2×3 + 11×2 + 35 is true? Any rational root of f(x) is a factor of 35 divided by a factor of 66. Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20×4 + x3 + 8×2 + x – 12?According to the Rational Roots Theorem, the statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 which is true is: Any rational root of f(x) is a factor of -49 divided by a factor of 25. The key points are "factors", and "ratio between the constant term and the coefficient of the highest order (exponent) term"

According to the Rational Root Theorem, which statement – according to the rational root theorem, which statement about f(x) = 12×3 – 5×2 + 6x + 9 is true? Questioned by maham237 @ 22/12/2020 in Mathematics viewed by 170 persons sarah is making a scale drawing of a painting that is 48 in wide by 120 in highAccording to the Rational Root Theorem, which number is a potential root of f(x) = 9x^8 + 9x^6 – 12x + 7?According to the Rational Roots Theorem, which statement about f(x) = 25×7 – x6 – 5×4 + x – 49 is true? Any rational root of f(x) is a factor of -49 divided by a factor of 25. What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?