Question

find the quadratic polynomial the sum of whose roots are √2 and their product is -12

Answer 1

Given : The sum of whose roots are √2 and their product is -12 .

Need To Find : The Quadratic Polynomial.

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As, We know that ,

• Quadratic Polynomial = x² - (sum of zeroes ) x + Product of zeroes

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Given that :

• The sum of roots are √2 and their product is -12

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⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

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⠀⠀⠀⠀⠀⠀$:\implies {\tt{ \bigg( x^{2} - \sqrt {2}x + (-12) \bigg) }}$

⠀⠀⠀⠀⠀⠀$:\implies {\tt{ \bigg( x^{2} - \sqrt {2}x - 12 \bigg) }}$

⠀⠀⠀⠀⠀⠀$:\boxed{\sf{ New\:Formed \:Quadratic \:Polynomial = x^{2} - \sqrt{2}x -12 }}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\: Formed \:Quadratic \:Polynomial = x^{2} - \sqrt{2}x -12 }}}$

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