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Question

Let α,β be two roots of the quadratic equation ax2+bx+c=0 then find the value of α2+β2.

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Solution

Given α,β be two roots of the quadratic equation ax2+bx+c=0.

Then from the relation between the roots and co-efficients we get,

α+β=ba .....(1) and

α.β=ca .....(2).

Now,

α2+β2

=(α+β)22α.β

=b2a22×ca [ Using (1) and (2)]

=b22aca2

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