Question

find a quadryic polynomial as the sum and product of its zeroes are -1/3 and 1/3respectivrly

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Answer 1

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Q1) Find a quadratic polynomial as the sum and products of its zeros are -1/3 and 1/3 respectively :)

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\: \large \green{ \bold{ \underline{step \: by \: step \: explaination}}}$

$\quad \bullet \underline{ \rm{by \: using \: formation \: of \: quadratic \: equation}}$

$\: \implies \displaystyle \sf{ \alpha = - \frac{1}{3} }$

$\: \: \implies \displaystyle \sf{ \alpha = \frac{1}{3} }$

$\: \: \implies \displaystyle \bf{ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0}$

$\: \: \\ \implies \displaystyle \sf{ {x}^{2} - \bigg( \frac{ - 1}{3} + \frac{1}{3} \bigg)x + \bigg( \frac{ - 1}{3} \times \frac{1}{3} \bigg) = 0}$

$\: \: \implies\displaystyle \sf{ {x}^{2} - (0)x + \frac{ - 1}{9} = 0}$

$\: \: \implies \displaystyle \sf{9 {x}^{2} - 1 = 0}$

$\: \: { \boxed{ \underline{ \bf \therefore \: the \: quadratic \: equation \: is \: 9 {x}^{2} - 1 = 0}}}$