Question

ef x³+6x²+ 4x + k is exactly divisible by x+ 2
then k.
a - 6
b) -2
c) -8. d)-10​

Answer 1

Given -

x³ + 6x² + 4x + k is divisible by x + 2 .

To find -

Find the required value of k for which the above condition holds .

Solution -

Let f ( x ) = x³ + 6x² + 4x + k

&

g ( x ) = x + 2 .

g ( 0 ) is -2.

Hence , f ( -2 ) = 0

=> [ -2 ]³ + 6 [ -2 ]² + 4 ( -2 ) + k = 0 .

Simplifying this -

=> [ -2 ]³ + 6 [ -2 ]² + 4 ( -2 ) + k = 0

=> ( -8 ) + 24 - 8 + k = 0

=> 24 - 16 + k = 0

=> 8 + k = 0

=> k = -8 .

Thus , for the value of k = -8 , x³+6x²+ 4x + k is exactly divisible by x+ 2 .

Hence , Option C is the correct answer .

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