Question

find a quadratic polynomial if the sum and product of zeroes are 2√3 and 2


Dont answer if u dont know plz​

Answer 1

Answer:

Given :-

• The sum and product of zeroes are 2√3 and 2.

To Find :-

• What is the quadratic polynomial.

Formula Used :-

$\clubsuit$ Quadratic Equation Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{x^2 - (Sum\: of\: roots)x + (Product\: of\: roots)}}}$

Solution :-

Given :

$\bigstar\: \: \bf Sum\: of\: roots\: (\alpha + \beta) =\: 2\sqrt{3}$

$\bigstar\: \: \bf Product\: of\: roots\: (\alpha\beta) =\: 2$

According to the question by using the formula we get,

$\footnotesize\mapsto \sf\bold{\green{x^2 - (Sum\: of\: roots)x + (Product\: of\: roots)}}$

$\footnotesize\longrightarrow \sf\bold{\purple{x^2 - (\alpha + \beta)x + (\alpha\beta)}}$

$\longrightarrow \sf x^2 - (2\sqrt{3})x + 2$

$\longrightarrow \sf\bold{\red{x^2 - 2\sqrt{3}x + 2}}$

${\small{\bold{\underline{\therefore\: The\: required\: quadratic\: polynomial\: is\: x^2 - 2\sqrt{3}x + 2\: .}}}}$

Answer 2

Given :-

• The sum of zeroes of the polynomial = 2√3
• The product of zeroes of the polynomial = 2

To Find :-

• The quadratic polynomial?

Solution

$( \alpha + \beta ) = 2 \sqrt{3} \: \: \: \: \: \: \: \: \: \: ...(Given)$

$(\alpha \beta ) = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(Given)$

For finding the quadratic equations, we use

$\footnotesize\red{{x}^{2}-(Sum \: of \: roots)x+(Product \: of \: roots)}$

$\longrightarrow \: {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )$

$\longrightarrow \: {x}^{2} - (2 \sqrt{3})x + 2$

$\longrightarrow \: {x}^{2} - 2 \sqrt{3} x \: + 2$

$\therefore \: The \: required \: polynomial \: is \\ {x}^{2} - 2 \sqrt{3} x \: + 2 \: \: \: \: \: \: \:$