Question

Find the quadratic polynomial whose sum and product of its zeroes are sqrt 2 and 0 respectively.​

Answer 1

Given :-

Sum and product of its zeroes are sqrt 2 and 0 respectively.​

To Find :-

Quadratic polynomial

Solution :-

We know that

α + β = -b/a

α + β = √2

αβ = c/a

αβ = 0

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

⇒ x² - (√2)x + 0

⇒ x² - √2x + 0

⇒ x² - √2x

Answer 2

Answer:

$\large \green{ \boxed{\sf \: The \: polynomial \: is \: : {x}^{2} - \sqrt{2} \: x}}$

Step-by-step explanation:

Given,

Sum of zeroes of quadratic polynomial = $\sqrt{2}$

and

Product of zeroes of quadratic polynomial = 0

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

$\sf \: \alpha + \beta = \sqrt{2} \: \: \: \: and\\ \sf \: \alpha \beta = 0 \\ \\ \bf so \: polynomial \: is \: \\ \\ \: \: \: \: \bf {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \bf = {x}^{2} - \sqrt{2} \: x + 0 \\ = \green {\bf {x}^{2} - \sqrt{2} \: x}$