If the sum of the roots of the equation
Asked by admin @ in Math viewed by 293 People
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
Answered by admin @
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 ( answer)
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