Question

find a and b such that x+2 and x-2 are factor of the polynomial ax^4+2x^3-3x^2+bx-4

Answer 1

Since x+2 & x-2 are factors so
x+2=0 & x-2=0 will give zero of polynomial, that is,
x=2 & -2 are zeros of given polynomial
Putting these values
x=2→16a+16-12+2b-4=0
16a+2b=0
8a+b=0
x=-2→16a-16-12-2b-4=0
16a-2b=32
8a-b=16

On solves these conditions we get
a=1, b=-8

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