Question

For what value of k, will the expression
(3(x)^3 – k(x)^2 + 4x + 16)
be divisible by (x - k/2) ?
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Answer 1

Answer:

Let f(x) = 3x3 – kx2 + 4x + 16. Then, f(x) will be divisible by ((x – k2k2)) if f(k2)(k2) = 0 ⇒ 3.(k2)(k2)3 – k.(k2)(k2)2 + 4(k2)(k2) + 16 = 0 ⇒ 3k383k38 - k34k34 + 4k24k2 + 16 = 0 ⇒ 3k3−2k3+16k+12883k3−2k3+16k+1288 = 0 ⇒ k3 + 16k + 128 = 0 ⇒ (k + 4) (k2 – 4k + 32) = 0 ⇒ k + 4 = 0 ⇒ k = – 4