Question

U by the square method. 39. Ifa, ß are the roots of the equation 2x2-3x - 4 = 0 form the equation whose root are 1/a²,1/ ß²


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Answer 1

Answer:

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Explanation:

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2x2−3x−4=2(x−α)(x−β)

=2x2−2(α+β)x+2αβ

From which we conclude that

α+β=32

αβ=−2.

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Given: α , β are the roots of 2x2−3x+4=0

Sum of the roots = α+β=32

Product of the roots = α.β=−42=−2

α2+β2=(α+β)2–2.α.β=(32)2−(2∗(−2))=254

αβ+βα=α2+β2α.β

=254∗(−2)=−258