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
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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)
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