Question

If X3 + 6x2 + kx + 6 is exactly divisible by (x+2),then k=?

Answer 1

Answer:

its 1marks I know Im also 9th my teacher teach this question the answer is 11

Answer 2

Given,

x3 + 6x2 + kx + 6 is exactly divisible by (x+2)

To Find,

The value of k

Solution,

$x + 2 = 0\\x = -2$

x3 + 6x2 + kx + 6 was divisible by x+ 2. therefore putting value of x as -2we get:

p(x)= $(x)^{3} + 6 *(x)^{2} +k*(x) +6$

p(-2) = $(-2)^{3} + 6 *(-2)^{2} +k*(-2) +6 = 0$

$(-2)^{3} + 6 *(-2)^{2} +k*(-2) +6 = 0\\(-8) + 6* (4) -2k + 6 =0\\2k = 24 -8 + 6 = 22\\k= 22/2 \\k= 11$

Hence, The value of k is 11.