Question

find a and b so that x²-1 is a factor of x⁴+ax³+2x²-3x+b.​

Answer 1

Answer:

F(x)=x⁴+ax³+2x²-3x+b

x+1=0 or x=-1.

f(-1)=(-1)⁴+a(-1)³+2(-1)²-3(-1)+b

=1-a+2+3+b

=6-a+b

(x+1) is a factor, Therefore reminder=0.

6-a+b=0 Or -a+b=-6 -- (eq1)

Again (x-1)=0 or x=1

f(1) = (1)⁴+a(1)³+2(1)²-3(1)+b

=1+a+2-3+b

=a+b=0 -- (eq2)

Adding 1&2

2b=-6

b=-3

From 2,

a=3

a=3, b=-3