Question

F(x)=x^4+mx^2+4, (x-1) is a factor, find m

Answer 1

m= -5

Explanation:

x⁴+mx²+4 =1* x⁴+0*x³+mx²+0*x+4

= (x-1) (x³+ax²+bx-4)

= x⁴ + (a-1)x³ + (b-a)x² - (b+4)x +4

(a-1)x³ vs 0*x³: a-1=0 a=1

- (b+4)x vs 0*x: - (b+4)=0 b= -4

(b-a)x² vs mx²: b-a = m = -4-1 = -5

Check: x-1=0 x=1

f(1) = 1⁴+ (-5)*1²+4 = 1-5+4 = 0