Question

if alpha and beta are the zeroes of p(x) = 4x^2+4x-1, then find
the value of 1÷alpha and 1÷beta​

Answer 1

$Answer \: \\ \\ Given \: \: Quadratic \: Polynomial \: \: is \\ \\ p(x) = 4x {}^{2} + 4x - 1 \\ \\ \alpha + \beta = \frac{ - 4}{4} \: \: \: \: \: and \: \: \: \: \: \alpha \beta = \frac{ - 1}{4} \\ \\ \alpha + \beta = - 1 \: \: \: \: \: \: \: and \: \: \: \: \: \alpha \beta = \frac{ - 1}{4} \\ \\ \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ - 1}{ \frac{ - 1}{4} } \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = 4 \\ \\ therefore \: \: \: \: \: \frac{1}{ \alpha } + \frac{1}{ \beta } = 4 \\ \\ Note \: \\ \\ for \: a \: General \: \: Quadratic \: polynomial \: say \\ \\ f(x) = ax {}^{2} + bx + c \\ \\ \alpha + \beta = \frac{ - b}{a} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \alpha \beta = \frac{c}{a}$