Q.180. Quadratic equation.

Question 180.
If a(p+q)^2 + 2bpq + c=0 and a(p+r)^2 +2bpr + c = 0,
then find the value of qr.

Answer 180.
a(p+q)^2 + 2bpq + c = 0 and a(p+r)^2 +2bpr + c = 0
=> aq^2 + 2p(a+b)q + ap^2 + c = 0
and ar^2 + 2p(a+b)r + ap^2 + c = 0


=> q and r are the roots of the equation
ax^2 + 2p(a+b)x + ap^2 + c = 0
=> qr = (ap^2 + c) / a.

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