Question

Form a quadratic polynomial whose sum & product of the 0 are-1 & 2

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Equation=x^{2}+x+2=0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt:{ \implies Sum \: of \: zeroes = -1} \\ \\ \tt: \implies Product \: of \: zeroes = 2 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Quadratic \:equation = ?$

• According to given question :

$\circ \: \tt{Let \: \alpha \: and \: \beta \: be \: the \: zeroes} \\ \\ \tt \circ \: sum \: of \: zeroes = -1\\ \\ \tt: \implies \alpha + \beta = -1 \\ \\ \tt \circ \: product \: of \: zeroes = 2 \\ \\ \tt: \implies \alpha \beta = 2 \\ \: \\ \bold{As \: we \: know \: that} \\ \tt: \implies {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) = 0\\ \\ \tt: \implies {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ \text{Putting \: given \: values} \\ \tt: \implies {x}^{2} - (-1)\times x + 2= 0 \\ \\ \green{\tt: \implies {x}^{2} +x +2 = 0}$

Answer 2

AnswEr:-

Quadratic polynomial = x² + x + 2

$\rule{200}{1}$

Given:-

☛ Sum of zeroes = -1

☛ Product of zeroes = 2

To find:-

☛ Quadratic polynomial = ?

Solution:-

Let the zeroes of polynomial be α & β

The standard form of an quadratic polynomial is :-

☛ x² - (Sum of zeroes)x + Product of zeroes

↠ x² - (α + β)x + αβ

Here,sum of zeroes = -1

∴ α + β = -1

And,product of zeroes = 2

∴ αβ = 2

$\rule{200}{1}$

⋆ QUADRATIC POLYNOMIAL:-

⇒ x² - (-1)x + (2)

⇒ x² + 1x + 2

⇒ x² + x + 2

∴ Quadratic polynomial = x² + x + 2