If p and q are the roots of the equation ax^2 + bx + c = 0, find the value - Maths - Linear Inequalities

Question

If p and q are the roots of the equation ax^2 + bx + c = 0, find
the value of 1/(ap^2+c)^2 + 1/(aq^2+c)^2

Aarushi Mishra · Accepted Answer

If p and q are roots of the equation ax2+bx+c=0 thenap2+bp+c=0ap2+c=-bpaq2+bq+c=0aq2+c=-bq1ap2+c2+1aq2+c2=1-bp2+1-bq2=1b21p2+1q2=1b2p2+q2p2q2=1b2p2+q2pq2=1b2p2+q2+2pq-2pqpq2=1b2p+q2-2pqpq2Using formula for sum and product of rootsp+q=-bapq=ca=1b2-ba2-2caca2=1b2b2a2-2cac2a2=1b2b2-2aca2c2a2=1b2b2-2acc2=b2-2acb2c2

If p and q are the roots of the equation ax^2 + bx + c = 0, find the value of 1/(ap^2+c)^2 + 1/(aq^2+c)^2.