Given the function: f(x) = 5×3+8×2−7x−6 Using the Rational Root Theorem, name 4 possible roots of the function and

Question

Given the function:

f(x) = 5×3+8×2−7x−6

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

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    2021-10-14T01:53:45+00:00

    Answer:

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

    Step-by-step 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.

    _____

    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.

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