Question

Find the quadratic polynomial , the sum of whose zeroes is square root 2and there product is -12

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{x^{2}-\sqrt{2}x-12=0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Sum \: of \: zeroes = \sqrt{2} \\ \\ \tt: \implies Product \: of \: zeroes = - 12 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Quadratic \: eqn = ?$

• According to given question :

$\tt \circ \: Let \: zeroes \: be \: \alpha \: and \: \beta \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Sum \: of \: zeores = \sqrt{2} \\ \\ \tt: \implies \alpha + \beta = \sqrt{2} \\ \\ \tt: \implies Product \: of \: zeores = - 12 \\ \\ \tt: \implies \alpha \beta = - 12 \\ \\ \bold{For \: quadratic \: eqn : } \\ \tt: \implies {x}^{2} - (Sum \: of \: zeroes) x + (Product \: of \: zeroes)=0 \\ \\ \tt: \implies {x}^{2} - ( \alpha + \beta )x + \alpha \beta=0 \\ \\ \tt: \implies {x}^{2} - \sqrt{2} x + ( - 12) = 0 \\ \\ \green{\tt:\implies {x}^{2} - \sqrt{2} x - 12 = 0}$

Answer 2

$\tt{\huge{\red{Hello !!! }}}$

QUESTION :

Find the quadratic polynomial , the sum of whose zeroes is square root 2and there product is -12.

SOLUTION :

A Quadratic Polynomial can be expressed as

X^2 - (Sum of Zeroes ) + (Product of Zeroes )

Hence the required Polynomial becomes :

X^2 - √2x - 12.