Question

obtain all the zeroes of x⁴+2x³-7x²-8x+12 if two of its zeroes are 2 and -2​

Answer 1

Step-by-step explanation:

Let,

p(x): x⁴+2x³-7x²-8x+12

given

2 and -2 are two zeros of the polynomial p(x)

(x-2) and (x+2) are two factors of the polynomial

(x-2) (x+2)=(x)²-(2)²=x²-4 is a factor of the polynomial

DIVIDING x⁴+2x³-7x²-8x+12 by x²-4 we get

x²+2x-3 by using middle term factoriasation

x²+2x-3= x²+(3-1)-3=x²+3x-x-3=x(x+3)-1(x+3)

=(x+3) (x-1)

therefore the other two zeroes are x=-3 and x=1

HOPE IT WILL HELP YOU