Question
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 = 58and H = 87
x2 – 2 × 58 x + 58× 87= 0 ̃ 5x2 –16x + 7 = 0