Question

obtain all the zeroes of polynomial f(x) =2x3-7x2+3x-6, if it's two zeroes are-√3/2, √3/2​

Answer 1

x-√3/2)(x+√3/2)=x²-3/2

g(x)=x²-3/2

p(x)=2x^4-2x³-7x²+3x+6

then q(x)=2x²-2x-4

⇒2x²-2x-4=2x²+2x-4x-4=2x(x+1)-4(x+1)=(2x-4)(x+1)

⇒2x-4=0         or               ⇒  x+1=0

⇒x=2               or                ⇒  x= -1