Question

if x2+4x+k is exactly divisible by x+2,then k is​

Answer 1

GIVEN :-

• x² + 4x + k is exactly divisible by x + 2.

TO FIND :-

• The value of k.

SOLUTION :-

Let x + 2 = 0

↬ x = -2

✮ In question it is given that , x² + 4x + k is exactly divisible by x + 2 . So we can say that,

➳ x² + 4x + k = 0

➳ (-2)² + 4 × (-2) + k = 0

➳ 4 + (-8) + k = 0

➳ 4 - 8 + k = 0

➳ -4 + k = 0

➳ k = 4

Hence required value of k is 4.

✮ Verification,

➳ x² + 4x + k = 0

➳ (-2)² + 4 × (-2) + 4 = 0

➳ 4 + (-8) + k = 0

➳ 4 - 8 + 4 = 0

➳ 8 - 8 = 0

➳ 0 = 0

Hence Verified.

Answer 2

$\huge\fcolorbox{red}{lime}{Question}$

If x² + 4x + k is exactly divisible by x + 2,then k is

$\huge\fcolorbox{red}{lime}{Solution}$

Given,

x = 2 => x = -2

Now, we have to substitute-2 in the equation.

x² + 4x + k = 0

(-2)² + 4(-2) + k = 0

4 + (-8) + k = 0

-4 + k = 0

k = 4

Verification:-

x² + 4x + k = 0

(-2)² + 4(-2) + 4 = 0

4 + (-8) + 4 = 0

8 - 8 = 0

0 = 0

Hence the value of k = 0

Extra Information:-

If the equation is x³ + 6x² + 4x + k by x + 2

[ given in the picture ]