If A.M. of the roots of a quadratic equation is 8/5 and A.M. of their reciprocals is 8/7, then the equation is

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5x2-16x+7=0

7x2-16x+5=0

7x2-16x+8=0

3x2-12x+7=0

answer is A.

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Detailed Solution

Let the roots are α and β⇒α+β2=85⇒α+β=165 ...(i)and 1α+1β2=87⇒α+β2αβ=87⇒(16/5)2(8/7)=αβ⇒αβ=75 ...(ii)∴ Equation is x2-(165)x+75=0 ⇒5x2-16+7=0

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