Question

if alpha and beta are the zeroes of x2+7x+12 then find the value of 1/alpha+1/beta-2alphabeta
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Answer 1

⠀⠀⠀☛...Given...☚

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quadratic polynomial = x² + 7x + 12

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⠀⠀⠀ ☛...To find...☚⠀⠀

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The value of $\dfrac{1}{ \alpha } + \dfrac{1}{ \beta } - 2 \alpha \beta$⠀

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⠀⠀⠀☛...Solution...☚⠀

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We know that...

$\:Sum\: of\: zeroes\: =\dfrac{-coefficient \:of \:x}{coefficient \:of\: x^{2}}$

• alpha + beta = -7⠀⠀

$\:Product \:of \:zeros\: = \dfrac{-coefficient\: of\: constant\: term}{coefficient \:of \:x^{2}}$

• alpha + beta = 12

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So...

• $\dfrac{1}{ \alpha } + \dfrac{1}{ \beta } - 2 \alpha \beta$

• $\dfrac{ \alpha + \beta} {\alpha × \beta}- 2 \alpha \beta$

• $\dfrac{ -7 } {12}- 2 × 12$

• $\dfrac{ -7 } {12}- 24$

• $\dfrac{ -296 } {12}$

• $\dfrac{ -148 } {6}$

• $\dfrac{ -74} {3}$