Question

Find the quadratic polynomial for which the sum of the roots is 7 and product of the roots is 12. *
X²+7x-12
X²+7x+12
X²-7x+12
X²-7x-12

Answer 1

Answer:

Given :-

• The sum and product of the roots is 7 and 12 respectively.

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 :

$\bigstar\: \: \bf Sum\: of\: roots\: (\alpha + \beta) =\: 7$

$\bigstar\: \: \bf Product\: of\: roots\: (\alpha\beta) =\: 12$

According to the question by using the formula we get,

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

$\footnotesize\longrightarrow \sf\bf x^2 - (\alpha + \beta)x + (\alpha\beta)$

$\longrightarrow \sf x^2 - (7)x + (12)$

$\longrightarrow \sf\bold{\red{x^2 - 7x + 12}}$

${\small{\bold{\underline{\therefore\: The\: required\: quadratic\: polynomial\: is\: x^2 - 7x + 12\: .}}}}$

Hence, the correct options is option no (c) x² - 7x + 12.