Question

Given the function:

f(x) = 5x3+8x2−7x−6

Using the Rational Root Theorem, name 4 possible roots of the function and show or describe how you found them.

Answer 1

±1/5, ±2/5, ±3/5, ±1, ±6/5, ±2, ±3, ±6

Explanation:

The rational root theorem tells you possible rational roots are ...

... ±(divisor of the constant term) / (divisor of the highest-degree term coefficient)

The constant term, -6, has divisors ±1, ±2, ±3, ±6. The coefficient of the highest degree term, 5, has divisors ±1, ±5. Possible ratios of these values are listed above.

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Roots of this Function

The coefficients sum to zero, so x=1 is a root. Factoring out (x-1) leaves a factor of 5x² +13x +6, which can be factored as (x+2)(5x+3). Hence the roots are -2, -3/5, +1 — all on the list of possible rational roots.