Question

if alpha and beta are the zeros of quadratic polynomial x square minus x minus 4 find the value of one upon alpha plus one upon beta minus alpha beta

Answer 1

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Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\huge{\underline{\bf{Given \: :}}}$

⟹ x² - x - 4

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$\huge{\underline{\bf{To \: Find \: :}}}$

$\sf{value \: of \: : \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta }$

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$\huge{\underline{\bf{Solution \: :}}}$

$\sf{ \alpha \: + \: \beta = \frac{ - b}{a} } \\ \\ \sf{ \alpha \: + \: \beta = 1 \: \: .....(1)} \\ \\ \bf{now} \\ \\ \sf{ \alpha \beta = \frac{c}{a} } \\ \\ \sf{ \alpha \beta = - 4 \: \: .....(2)}$

$\rule{200}{2}$

Now,

$\sf{ \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta } \\ \\ \sf{ \frac{ \beta \: + \: \alpha}{ \alpha \beta} - \alpha \beta} \\ \\ \bf{from \: equation \: 1 \: and \: 2} \\ \\ \sf{ \frac{1}{ - 4} - ( - 4) } \\ \\ \sf{ \frac{ - 1}{4} + \frac{4}{1} } \\ \\ \sf{ \frac{ - 1 + 16}{4} } \\ \\ \sf{ \frac{ - 15}{4} }$

$\large{ \boxed{ \orange{ \sf{\frac{-15}{4}}}}}$