Question

Find a quadratic polynomial, the sum and product of whose zeros are 3 and 2 respectively​

Answer 1

Answer:

     x² - 5x + 6

Step-by-step explanation:

∝ = 3  ,  β = 2

Quadratic Equation - x² - x(∝+β) + ∝β

  x² - x(∝+β) + ∝β

= x² - 5x + 6

Answer 2

Answer:

Given :-

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

To Find :-

• What is the quadratic polynomial.

Formula Used :-

$\clubsuit$ Quadratic Polynomial Formula :

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

Solution :-

Given :

$\bigstar\: \bf Sum\: of\: roots\: (\alpha + \beta) =\: 3$

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

According to the question by using the formula we get,

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

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

By putting α + β = 3 and αβ = 2 we get,

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

$\longrightarrow \sf x^2 - 3x + 2$

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

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