Question

are 1) Find ta quadratic polynomial, if the sum and product of whose zeroes -2 and 5 respectively​

Answer 1

Given :-

If the sum and product of whose zeroes -2 and 5 respectively​

To Find :-

Quadratic polynomial

Solution :-

We know that

α + β = -b/a

α + β = -2(i)

αβ = c/a

αβ = 5(ii)

Quadratic polyomial = x² - (α + β)x + αβ

⇒ x² - (-2)x + 5

⇒ x² + 2x + 5

Answer 2

Answer:

$\: \: \: \: \: \large \green{ \boxed{ \bf {x}^{2} + 2x + 5}} \pink{\longrightarrow \sf \: answer}$

Step-by-step explanation:

Given,

Sum of zeroes of quadratic polynomial = - 2

and

Product of zeroes of quadratic polynomial = 5

We have to find :

The quadratic polynomial

Method :

General formula of quadratic polynomial is :

$\pink{ \small{ \bf \: {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes}}$

Here,

Sum of zeroes can be represented by $\alpha + \beta$

and

Product of zeroes can be represented by $\alpha \beta$

Solution :

According to the question, we can write that

$\sf \: \alpha + \beta = - 2 \: \: \: \: and\\ \sf \: \alpha \beta = 5$

So the polynomial is :

$\: \: \: \bf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \bf \ = {x}^{2} - ( - 2)x + 5 \\ \bf \: = {x}^{2} + 2x + 5$