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

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Example Questions

Example Question #1 : Descartes' Rule, Intermediate Value Theorem, Sum And Product Of Zeros

Given $\displaystyle y=5x^2+14x-3$ , determine the sum and product of the zeros respectively.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

To determine zeros of $\displaystyle y=5x^2+14x-3$ , factorize the polynomial.

$\displaystyle 5x^2+14x-3=(5x-1)(x+3)$

Set each of the factorized components equal to zero and solve for $\displaystyle x$ .

5x-1=0 $\displaystyle 5x-1=0$

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

x+3=0 $\displaystyle x+3=0$

x=-3 $\displaystyle x=-3$

The sum of the roots:

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

The product of the roots:

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

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Example Question #431 : Pre Calculus

Please choose the best answer from the following choices.

Find the sum and product of the zeros of the following polynomial:
$\displaystyle x^2-5x+6$

Possible Answers:

Sum=1 $\displaystyle Sum=1$

$\displaystyle Product=3/2$

Sum=5 $\displaystyle Sum=5$

$\displaystyle Product=6$

Sum=1 $\displaystyle Sum=1$

$\displaystyle Product=5$

Sum=-5 $\displaystyle Sum=-5$

$\displaystyle Product=6$

Correct answer:

Sum=5 $\displaystyle Sum=5$

$\displaystyle Product=6$

Explanation:

To find the zeros you have to factor the polynomial.

This is easily factorable and you will get (x-3) $\displaystyle (x-3)$ and (x-2) $\displaystyle (x-2)$ .

Next, set both of these equal to zero. x-3=0 $\displaystyle x-3=0$ and x-2=0 $\displaystyle x-2=0$ .

Isolate the x's and you will get x=3 $\displaystyle x=3$ and x=2 $\displaystyle x=2$ .

The sum will be $\displaystyle 5$ since you add the two together, and the product will be $\displaystyle 6$ because you multiply the two together.

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

Please choose the best answer from the following choices.

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

$\displaystyle 4x^2+15x+11$

Possible Answers:

$\displaystyle Sum=-15/4$

$\displaystyle Product=-11/4$

$\displaystyle Sum=-15/4$

$\displaystyle Product=11/4$

$\displaystyle Sum= -7/4$

$\displaystyle Product=11/4$

$\displaystyle Sum= 15/4$

$\displaystyle Product= 11/4$

Correct answer:

$\displaystyle Sum=-15/4$

$\displaystyle Product=11/4$

Explanation:

Factoring the polynomial will give you (4x+11) $\displaystyle (4x+11)$ and (x+1) $\displaystyle (x+1)$ .

The zeros of these binomials will be x=-11/4 $\displaystyle x=-11/4$ and x=-1 $\displaystyle x=-1$ .

If you add these together (sum) you get -15/4 $\displaystyle -15/4$ and if you multiply them together (product) you get 11/4 $\displaystyle 11/4$ .

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

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Descartes' Rule, Intermediate Value Theorem, Sum And Product Of Zeros

Example Question #431 : Pre Calculus

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

All Precalculus Resources

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