Question

Find a quadratie polynomial
the sum and product of whose zeroes are -3 and 2 respectively​

Answer 1

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Question :

Find a quadratic polynomial the sum and products of whose zeroes are -3 and 2 respectively.

To find :

the quadratic equation =?

Given :

$\: \normalsize \bullet \bf \: \alpha = - 3 \: \: and \: \: \: \beta = 2$

Formula :

By using formation of quadratic equation :

$\\ \: \therefore\large \boxed{ \sf{ \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0}}$

$\\ \large\sf{\underline{\color{orange} Solution :}}$

$\\ \implies \sf \: \alpha = - 3 \: \: and \: \beta = 2 \: \: \: ....given$

$\\ \implies \sf \: {x}^{2} - ( - 3 + 2)x + ( - 3)(2) = 0$

$\\ \implies \sf {x}^{2} - ( - 1)x - 6 = 0$

$\\ \implies \sf \: {x}^{2} + x - 6 = 0$

The Quadratic equation will be x²+x-6=0

Additional information :

• For Finding the roots of quadratic equation we use formula method

$\boxed{\large{\sf{x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}}}}$

• The quadratic equation is always in the form of ax²+bx+c=0 where a is greater than 0 it's domains is real number.