Question

Find quardatic polynomial with zero -2 and 1/3

Answer 1

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TO DETERMINE

A quadratic polynomial the sum and product of whose zeroes are

$\sf{\displaystyle \: - 2 \: \: and \: \: \frac{1}{3} \: \: respectively }$

TO FIND

The quadratic polynomial

FORMULA TO BE IMPLEMENTED

The quadratic polynomial whose zeroes are given can be written as

${x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros)$

EVALUATION

The required Quadratic polynomial is

$= {x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros)$

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

$\sf{\displaystyle \: = {x}^{2} + \frac{5x}{3} - \frac{2}{3} \: }$

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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

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