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

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

A

7x2 + 16x + 5 = 0

B

7x2– 16x + 5 = 0

C

5x2 – 16x + 7 = 0

D

5x2 – 8x + 7 = 0

Answer

5x2 – 16x + 7 = 0

Explanation

Solution

α+β2\frac { \alpha + \beta } { 2 } = 85\frac { 8 } { 5 } ̃ a + b = 16/5 1α+1β2\frac { \frac { 1 } { \alpha } + \frac { 1 } { \beta } } { 2 } = 87\frac { 8 } { 7 }

̃ a+b/ab=16/7̃ ab =7/5x2–16/5x+7/5=0

̃5x2–16x+7=0