Question

if 3 is one zero of p(x)=x^2+kx-9.find the value of k​

Answer 1

Step-by-step explanation:

putting x=3 in x²+kx-9

3²+k×3-9=0

9+3k-9=0

3k=0

k=0/3

k=0

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Answer 2

k=0 ; if 3 is one of the zero of polynomial.

Given:

• A polynomial.
• $p(x) = {x}^{2} + kx - 9$

To find:

• If 3 is one zero of p(x), then find the value of k.

Solution:

Concept/Theorem to be used:

1. Factor Theorem: It states that if (x-a) is a factor of polynomial p(x), then p(a)=0.
2. Thus, If x=a is a zero of polynomial, then p(a)=0.

Step 1:

Put x=3 in the polynomial.

As x= 3 is a zero of polynomial,so p(3)=0

$p(3) = ( {3)}^{2} + 3k - 9$

or

$9 + 3k - 9 = 0$

Step 2:

Solve for k.

$9 + 3k - 9 = 0$

or

$3k = 0$

or

$\bf \red{k = 0}$

Thus,

Value of k=0 ; if 3 is one of the zero of polynomial.

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