Precalculus : Find the Sum and Product of the Zeros of a Polynomial

Example Questions

Example Question #1 : Find The Sum And Product Of The Zeros Of A Polynomial

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

Explanation:

To determine zeros of , factorize the polynomial.

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

The sum of the roots:

The product of the roots:

Example Question #2 : Find The Sum And Product Of The Zeros Of A Polynomial

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.

Example Question #3 : Find The Sum And Product Of The Zeros Of A Polynomial

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 .