Question

Find the quadratic polynomial
whose zeroes are
-2√3 and -√3/2?​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

A quadratic polynomial the sum and product of whose zeroes are

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

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

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

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

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

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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

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