Question

find the value of k , if x + 2 is a factor of 5 x to the power 2 + kx + 1 . Please solve this question..​

Answer 1

Step-by-step explanation:

Given -

• x + 2 is a factor of 5x² + kx + 1

To Find -

• Value of k

As we know that :-

• If x + 2 is a factor of polynomial then x = -2 is zero of that polynomial

→ p(x) = 5x² + kx + 1 = 0

→ p(-2) = 5(-2)² + k(-2) + 1 = 0

→ 20 - 2k + 1 = 0

→ 2k = 21

→ k = 21/2

Hence,

The value of k is 21/2

Verification :-

→ 5x² + 21x/2 + 1

→ 10x² + 21x + 2

→ 10x² + 20x + x + 2

→ 10x(x + 2) + 1(x + 2)

→ (10x + 1)(x + 2)

Here, the factor comes same as given in the question.

It shows that our answer is absolutely correct.

Answer 2

GIVEN:

• x + 2 is a factor of polynomial 5x² + kx + 1

TO FIND:

• k = ?

SOLUTION:

x + 2 is a factor that means x = - 2

p(x) = 5x² + kx + 1

Putting x = - 2

→ p(-2) = 5(-2)² + k(-2) + 1 = 0

→ p(-2) = 5(4) - 2k + 1 = 0

→ p(-2) = 21 - 2k = 0

→ k = 21/2

Hence, k = 21/2