Find the Sum and Product of the Zeros of a Polynomial

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Pre-Calculus › Find the Sum and Product of the Zeros of a Polynomial

Questions 1 - 3

1

Please choose the best answer from the following choices.

Find the sum and product of the zeros of the following polynomial:

Explanation

Factoring the polynomial will give you and .

The zeros of these binomials will be and .

If you add these together (sum) you get and if you multiply them together (product) you get .

2

Given , determine the sum and product of the zeros respectively.

$-\frac{14}{5},-\frac{3}{5}$

$\frac{1}{5},-3$

$\frac{16}{5}, -\frac{3}{5}$

$\frac{7}{5},-\frac{21}{5}$

$\frac{14}{5},-\frac{3}{5}$

Explanation

To determine zeros of , factorize the polynomial.

Set each of the factorized components equal to zero and solve for .

$x=\frac{1}{5}$

The sum of the roots:

$\frac{1}{5}+(-3)= \frac{1}{5}-\frac{15}{5}= -\frac{14}{5}$

The product of the roots:

$(\frac{1}{5})(-3)= -\frac{3}{5}$

3

Please choose the best answer from the following choices.

Find the sum and product of the zeros of the following polynomial:

Explanation

To find the zeros you have to factor the polynomial.

This is easily factorable and you will get and .

Next, set both of these equal to zero. and .

Isolate the x's and you will get and .

The sum will be since you add the two together, and the product will be because you multiply the two together.

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