Question

write a quadratic polynomial the sum of whose zero is 2 and product is -8​

Answer 1

SOLUTION :

TO DETERMINE

The quadratic polynomial the sum and product of whose zeroes are 2 and - 8 respectively

FORMULA TO BE IMPLEMENTED

The quadratic polynomial whose zeroes are given can be written as

$\sf{ {x}^{2} - (Sum \: of \: the \: zeros)x + (Product \:of \: the \: zeros)}$

EVALUATION

Here it is given that the sum and product of zeroes of a quadratic polynomial are 2 and - 8 respectively

Hence The required Quadratic polynomial is

$\sf{ {x}^{2} - (Sum \: of \: the \: zeros)x + (Product \:of \: the \: zeros)}$

$= \sf{ {x}^{2} - 2x - 8\: }$

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ADDITIONAL INFORMATION

A general equation of quadratic equation is

$a {x}^{2} + bx + c = 0$

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

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