Question

0 and -√2 are the zeros form the equation​

Answer 1

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

TO DETERMINE

A quadratic equation whose zeroes are 0 and -√2 respectively

FORMULA TO BE IMPLEMENTED

The quadratic equation whose zeroes are given can be written as

${x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros) = 0$

EVALUATION

The required Quadratic Equation is

${x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros) = 0$

$\implies \: {x}^{2} - ( - \sqrt{2} + 0)x + ( - \sqrt{2} \times 0) = 0$

$\implies \: {x}^{2} + \sqrt{2} x = 0$

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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

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