Question

please answer this question (please explain it step by step) plz urgent​

Answer 1

$\pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \:given \: the \: polynoial \\ \bf \: f(x) = {x}^{2} - x - 4 \: \\ \bf \: whose \: zeroes \: \: are \: \: \alpha \: \: and \: \: \beta \\ \\ \small{\orange{{\boxed{\begin{array}{cc} \small{\bf \: sum \: of \: zeroes \: \alpha + \beta = - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} } } \\ \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - \frac{ - 1}{1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 \\ \\ \bf \: product \: of \: zeroes \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } \\ \\ = \frac{ - 4}{1} \\ \\ = - 4\: \: \end{array}}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{\downarrow}\end{array}}}}$

${ \qquad\boxed{\boxed{\begin{array}{cc} \maltese \bf \: now \\ \\ \bf \: \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta \: \\ \\ = \frac{ \alpha + \beta - { (\alpha \beta )}^{2} }{ \alpha \beta } \\ \\ = \frac{1 - ( { - 4})^{2} }{ - 4} \\ \\ = \frac{1 - 16}{ - 4} \\ \\ = \frac{ - 15}{4} \\ \\ = \sf \: option \: (b)\end{array}}}}$