Relation between Roots and Coefficients for Quadratic
If α,β are th...
Question
If α,β are the roots of the equation 2x2−3x−6=0, then the equation whose roots are α2−1 and β2−1 is
A
2x2−25x−7=0
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B
4x2−25x+7=0
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C
2x2−17x+7=0
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D
4x2−17x+7=0
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Solution
The correct option is B4x2−25x+7=0 Let α2−1=y⇒α=±√y+1
Now, α is the root of the equation 2x2−3x−6=0, so 2α2−3α−6=0 ⇒2(±√y+1)2−3(±√y+1)−6=0 ⇒2y+2−6=(±3√y+1) ⇒2y−4=(±3√y+1)
Squaring on both sides, we get ⇒4y2−16y+16=9(y+1) ⇒4y2−25y+7=0