Question

Find the quadratic polynomial whose sum and product of zeroes are 4 and -4.​

Answer 1

Answer:

Given :-

• The sum and product of zeroes are 4 and - 4.

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 :

➲ Sum Of Roots (α + β) = 4

➲ Product Of Roots (αβ) = - 4

According to the question by using the formula we get,

$\small\longrightarrow \sf\bold{\purple{x^2 - (Sum\: Of\: Roots)x + (Product\: Of\: Roots)}}$

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

$\longrightarrow \sf x^2 - (4)x + (- 4)$

$\longrightarrow \sf\bold{\red{x^2 - 4x - 4}}$

${\small{\bold{\underline{\therefore\: The\: required\: quadratic\: polynomial\: is\: x^2 - 4x - 4\: .}}}}$

Answer 2

Step-by-step explanation:

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