Question

if alpha and beta are roots of quadratic equation X square - 8 x + 15 equal to zero find the value of 1/alpha + 1/ beta -2 alpha beta

Answer 1

you may know that for an quadratic eq a$x^{2}$+bx+x=0

α+β=$\frac{-b}{a}$=8

αβ=$\frac{c}{a}$=15

$\frac{1}{\alpha }$+$\frac{1 }{\beta }$-2$\alpha \beta$

taking Lcm we get

$\frac{\beta+\alpha -2\alpha ^{2} \beta ^{2} }{\alpha\beta  }$

inserting values

$\frac{8-2(15^{2} )}{15}$

solve and get the answer

Answer 2

$for \: the \: quadratic \: eqn \\ a {x}^{2} + bx + c = 0 \\ sum \: of \: roots = \frac{ - b}{a} = \alpha + \beta \\ product \: of \: roots = \frac{c}{a} = \alpha \beta \\ now \: given \\ {x}^{2} - 8x + 15 = 0 \\ \alpha + \beta = 8 \\ \alpha \beta = 15 \\ now \\ \frac{1}{ \alpha } + \frac{1}{ \beta } - 2 \alpha \beta \\ = \frac{ \alpha + \beta }{ \alpha \beta } - 2 \alpha \beta \\ = \frac{ - 442}{15}$
hope it helps