Question

Find all the zeroes of the polynomial 2x^4-9x^3+5x^2+3x-1 , if two of its zeroes are 2 + root 3 and 2-root3

Answer 1

Solution

q(x)=2x4−3x3−3x2+6x−2

q(x)=p(x)⋅(x−2–√)(x+2–√)

q(x)=p(x)⋅(x2−2)

bu using identity (x+a)(x−a)=x2−a2

p(x)=q(x)x2−2

=2x4−3x3−3x2+6x−2x2−2

by dividing , we get p(x)=2x2−x+1

=2x2−2x−x+1

=2x2−2x−x+1

=2x[x−1]−1[x−1]

p(x)=(x−1)(2x−1)