Question

What is the value of polynomial x2 + 8x + k , if -1 is a zero of the polynomial?
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Answer 1

p(X) = x^2 + 8x + k

given that X=-1 is the zero of above polynomial,

substituting in place of X

p(-1) = (-1)^2 + 8(-1) + k = 0

= 1 - 8 + k=0

= k = 7

Answer 2

The value of $\bf \red{k=7}$ and polynomial is $\bf \red{x^2+8x+7}$.

Given:

• ${x}^{2} + 8x + k \:$

To find:

• if -1 is a zero of polynomial then, what is the value of polynomial?

Solution:

Concept to be used:

If x=a is a zero of polynomial than it must satisfy the polynomial.

Step 1:

As -1 is the zero of polynomial.

Put x= -1 in the polynomial.

$( { - 1)}^{2} + 8( - 1) + k = 0$

or

$1 - 8 + k = 0$

or

$- 7 + k = 0$

or

$\bf k = 7$

Step 2:

Put the value of k in the polynomial.

${x}^{2} + 8x + 7$

Thus,

The value of k=7 and polynomial is x²+8x+7.

Learn more:

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