If a and are the roots of the equation ax² + bx + c = 0. then find the quadratic equations having the following pairs of roots: 1/alpha+ beta,1/alpha+1/beta
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Answer:
ax2+bx+c=0
α+β=a−b αβ=ac
(i) equation whose roots are α21,β21
Sum of roots =α21+β21=(αβ)2α2+β2=(αβ)2(α+β)2−2αβ)
=a2c2a2b2−a2c=c2b2−2ac\
product =α
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