Question

If x+2k is a factor of f(x)=x5-4k2x3+2x+2k+3,find k

Answer 1

Solution is attached below

Answer 2

Answer:

Value of $k = \frac{3}{2}$

Explanation:

If (x+2k) is a factor of

$f(x)=x^{5}-4k^{2}x^{3}+2x+3$ then Remainder f(-2k) = 0

Now ,

$f(-2k)=(-2k)^{5}-4(-2k)^{2}x^{3}+2(-2k)+2k+3=0$

/* By Factor theorem */

$\implies -32k^{5}-4(k^{2})(-2k)^{3}+2(-2k)+2k+3=0$

$\implies -32k^{5}+4k^{2}\times (-8)k^{3}-4k+2k+3=0$

$\implies -32k^{5}-32k^{5}-4k+2k+3=0$

$\implies -4k+2k+3=0$

$\implies -2k+3=0$

$\implies -2k=-3$

$\implies k =\frac{-3}{-2}$

$\implies k = \frac{3}{2}$

Therefore,

Value of $k=\frac{3}{2}$

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