Question

If alpha,beta are zeroes of the quadratic polynomial ax²+bx+c,then evaluate
1/(a*alpha+beta)+1/(alpha*beta+b)
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Answer 1

Answer:

ax2+bx+c=0

α+β=−b/a,αβ=c/a

From the first equation you get: α2+2αβ+β2=b2a2

Then you subtract 4αβ, which is 4c/a: α2−2αβ+β2=b2a2−4ca=b2−4aca2

Take square root of both sides(don’t forget the plus minus) α−β=±b2−4ac−−−−−−−√a