Question

if x= 2 is factor of x^5+ 4 k² x³ + 2x+ 2k +3 then find k

Answer 1

Hi friends

If x= 2 is a factor of the equation
so put it we get

${2}^{5} + 4 \times {k}^{2} \times {2}^{3} + 2 \times 2 + 2k + 3 = 0 \\ 32 + 32 {k}^{2} + 4 + 2k + 3 = 0 \\ 32 {k}^{2} + 2k + 39 = 0$
Here
$k = \frac{ - 2 + \sqrt{4 - 4 \times 32 \times 39} }{2 \times 32}$
Hope it helps you