Question

if x + 2 k is a factor of f(x) =x^4- 4 k^2+x^2 + 2 x + 3 k + 3 find k

Answer 1

hey !!!

x + 2 = 0

x = -2

f(x) = x⁴ - 4k² + x² + 2x + 3k + 3

f(-2) = (-2)⁴ - 4k² + ( -2) ² +2 ( - 2) + 3k + 3

=> 16 - 4k² + 4 -4 + 3k + 3

=> - 4k² +3k + 19

=> now by using quadratic formula ..

roots = -b +- (√b²-4ac /2a

roots = -3 +-(√3²- 4(-4)×19/2×-4

roots = -3 +-(√9-304/-8

roots = -3 +-√-295/-8

1 value of k '= -3+(√-295/ -8

k = -( 3 +√295 ) /-8

k = (3 +√295)/8

and 2nd value of k = -3 - (√-295 /-8

k = -3 + 295/-8

k = -( 3 -√295/ -8

k = 3 - √295/ 8

hope it helps !!!

₹Rajukumar111