Question

If alpha beta are the zeros of polynomial f(x)=ax2+bx+c, then find 1/a2+1/beta 2

Answer 1

Answer:

Heres your answer

$f(x) = a {x}^{2} + bx + c = 0 \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ \\ a = 1 \: b = 1 \: and \: c = 1$

$\alpha + \beta = \frac{ - b}{a} \\ \\ \alpha + \beta = - 1 \\ \\ \alpha \beta = \frac{c}{a} = 1$

$hence \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } = \frac{ - 1}{1} = - 1$

Hope it helps ✌