Question

Form a quadratic polynomial whose sum and product of its zeros are 10 and 3 respectively is​

Answer 1

Answer:

$\boxed{\bf \implies x^2-10x+3 }$

Step-by-step explanation:

$\text{sum of zeroes = 10} \\ \text{product of zeroes = 3} \\\\ \text{The quadratic polynomial is of the form,}\\\\ \implies x^2 - (sum \ of \ zeroes)x + (product \ of \ zeroes)\\ \implies x^2-10x+3$

Answer 2

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

TO DETERMINE

A quadratic polynomial the sum and product of whose zeroes are - 3 and 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

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

$= {x}^{2} - 10x + 3$

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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

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