Question

If alpha and beta are the zeroes of x²-x-4 then find the value of 1/alpha +1/beta -alpha xbeta

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 15}{4}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} - x - 4 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta =$

• According to given question :

$\bold{For \: sum \: of \: zeroes : } \\ \tt: \implies \alpha + \beta = \frac{ - b}{a} \\ \\ \tt: \implies \alpha + \beta = \frac{ - ( - 1)}{1} \\ \\ \green{\tt: \implies \alpha + \beta =1} \\ \\ \bold{For \: product \: of \: zeroes : } \\ \tt: \implies \alpha \beta = \frac{c}{a} \\ \\ \tt: \implies \alpha\beta = \frac{4}{1} \\ \\ \green{\tt: \implies \alpha \beta =4} \\ \\ \bold{For \: finding \: value : } \\ \tt: \implies \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta \\ \\ \tt: \implies \frac{ \alpha + \beta }{ \alpha \beta } - \alpha \beta \\ \\ \tt: \implies \frac{1}{4} - 4 \\ \\ \tt: \implies \frac{ 1 -16 }{4} \\ \\ \green{\tt: \implies \frac{ - 15}{4} } \\ \\ \green{ \tt \therefore \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 15}{4} }$