Question

if x²+4kx-9 is divisible by x+1,then the value of k is​

Answer 1

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Answer 2

Given :

• x² + 4kx - 9 is divisible by x +1

To find :

• Value of k .

Solution:

• When x + 1 completely divides x² + 4kx -9 , it is a root of the quadratic equation . Hence , it can be written in the form :

x + 1 = 0

x = -1

P(x) = x² + 4kx - 9

Substituting value of x = -1

P(-1) = (-1)² + 4k (-1) - 9

P(-1) = 1 - 4k -9

P(-1) = -4k - 8

Let P(-1) = 0

0 = -4k -8

4k + 8 = 0

4k = -8

k = -8/4

k = -2

Verification :

Substituting value of k = -2

P(-1) = (-1)² + 4 (-2) (-1) - 9

0 = 1 + 8 - 9

0 = 9 - 9

0 = 0

$\underline{\therefore \tt {Value\ of\ k\ is\ -2}}$