Question

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if alpha and beta are the roots of equation px²-mx+n=0, find the equation whose roots are alpha/beta and beta/alpha​

Answer 1

Answer:

The equation is

px2+qx+r=0

x2+qpx+rp=0

If α and β are the roots, then

the sum of the roots is α+β=−qp

and

the product of the roots is αβ=rp

=α2+β2=(α+β)2−2αβ=q2p2−2rp

The new roots are

(2α+1α) and (2β+1β)

Therefore, the sum of the roots is

(2α+1α)+(2β+1β)

=2(α+β)+(1α+1β)

=2(α+β)+α+βαβ

=(α+β)(2+

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