Question

if one zero of the cubic polynomial px^3+qx^2+rx+s is 2 then the square of the difference of other two zeroes is ?
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Answer 1

Answer:α+β+2=−qp

αβ+2β+2α=rp

2αβ=−sp

(α−β)2=α2+β2−2αβ

(α−β)2=(α+β)2−4αβ

α+β=−qp−2

(α−β)2=(α+β)2−4αβ

=(−qp−2)2−4(−s2p)

=(q+2pp)2+2sp

=q2+4p2+4pqp2+2sp

q2+4p2+4pqq+2psp2.

Explanation: