Question

write a quadratic polynomial.sum of whose zeroes is 2√5 and productis 5​

Answer 1

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

FORMULA TO BE IMPLEMENTED

If the zeroes of the quadratic polynomial are given, then the quadratic polynomial is obtained as

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

GIVEN

A quadratic polynomial, whose sum of zeroes are

$2 \sqrt{5}$

and product of zeros is 5

TO DETERMINE

The quadratic polynomial

EVALUATION

Sum of the zeroes

$= 2 \sqrt{5}$

Product of the Zeros = 5

So the required polynomial is

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

= ${x}^{2} - 2x \sqrt{5} + 5$