Relation between Roots and Coefficients for Quadratic
Let α, β are ...
Question
Let α,β are the roots of the equation 2x2−3x−7=0, then the quadratic equation whose roots are αβ and βα is
A
14x2+37x−14=0
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B
14x2−37x−14=0
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C
14x2−37x+14=0
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D
14x2+37x+14=0
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Solution
The correct option is D14x2+37x+14=0 2x2−3x−7=0
From the given equation, α+β=32,αβ=−72
When the roots are, αβ,βα
Sum of roots αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=94+7−72=−3714
Product of roots αβ×βα=1
Hence, required equation is x2+3714x+1=0∴14x2+37x+14=0