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Mathematics Question on Complex Numbers and Quadratic Equations

If α,β\alpha, \beta be the roots of x2−a(x−1)+b=0x^{2}-a(x-1)+b=0, then the value of 1α2−aα+1β2−aβ+2a+b\frac{1}{\alpha^{2}-a\alpha}+\frac{1}{\beta^{2}-a\beta}+\frac{2}{a+b} is

A

4a+b\frac{4}{a+b}

B

1a+b\frac{1}{a+b}

C

00

D

−1-1

Answer

00

Explanation

Solution

Since, α\alpha and β\beta are the roots of x2−ax+a+b=0x^{2} -ax + a+ b = 0, then