Question

Find a quadratic polinomial the sum and product are 1 and 1 respectively

Answer 1

Step-by-step explanation:

x²-(sum of zeroes)x+product of zeroes

x²-x+1

Answer 2

Answer:

Given :-

• The sum and product of a quadratic polynomial are 1 and 1 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 :

$\bigstar\: \: \bf{Sum\: of\: roots\: (\alpha + \beta) =\: 1}$

$\bigstar\: \: \bf{Product\: of\: roots: (\alpha\beta) =\: 1}$

According to the question by using the formula we get,

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

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

$\small\longrightarrow \sf x^2 - (1)x + 1$

$\small\longrightarrow \sf\bold{\red{x^2 - x + 1}}$

${\small{\bold{\underline{\therefore\: The\: required\: quadratic\: polynomial\: is\: x^2 - x + 1\: .}}}}$