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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

If A.M. and G.M. of roots are A, G then quadratic equation is x2 – 2Ax + G2 = 0

̃ x2 – 2Ax + AH = 0 \ A = 85\frac { 8 } { 5 }and H = 78\frac { 7 } { 8 }

x2 – 2 × 85\frac { 8 } { 5 } x + 85\frac { 8 } { 5 }× 78\frac { 7 } { 8 }= 0 ̃ 5x2 –16x + 7 = 0