Question

If the sum of the roots of the quadratic equation ax2+bx+c=0 is equal to the sum of the squares of their reciprocals then b2/ac + bc/a2 is equal to

Answer 1

Let P and Q are roots of eqn 

P + Q = -b/a 

PQ = c/a 

a/c to question, 

P + Q = 1/P² + 1/Q² 

-b/a ={ ( P + Q)²-2PQ }/P²Q² 

-b/a = { b²/a² -2c/a)/(c/a)² 

-b×c²/a³ = b²/a² -2c/a 

2c/a = b²/a² + bc²/a³ = b( ab + c²)/a³ 

2ca² = b²a + bc² 

2 = b²a/a²c + bc²/a²c 

= b²/ac + bc/a² 

b²/ac + bc/a² = 2