Question

A quadratic polynomial whose product of zeroes is -36 and sum of the zeroes is 0, is

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the quadratic polynomial.

$\huge\bf\underline \red{ \mathcal{S}olution..}$

$\bf\underline{\purple{Given:-}}$

• product of zeroes = -36
• sum of zeroes = 0

Let α and β be the zeroes of required polynomial.

• Let α + β = 0
• Let αβ = -36

Formula for quadratic polynomial :-

• x² -(α + β)x + αβ

⇛ x² -(0)x + (-36)

⇛ x² - 0x - 36

⇛ x² - 36

Hence,

• The required quadratic polynomial is x² - 36

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer

x² - 36

Given

Product of zeroes = - 36

Sum of zeroes = 0

To Find

Quadratic polynomial

Concept

General form of quadratic polynomial is ,

x² - (α+β)x + αβ

Solution

Let α , β be zeroes of polynomial .

So , Sum of zeroes ,

α + β = 0 ... (1)

Product of zeroes ,

αβ = - 36 ... (2)

So , Our required quadratic polynomial is ,

⇒ x² - (α+β)x + αβ

⇒ x² - (0)x + (-36)   [ From (1) & (2) ]

⇒ x² - 0 - 36

⇒ x² - 36

This is the required polynomial .

It can further be solved ,

⇒ x² - (6)²

⇒ (x+6)(x-6)

Since , a² - b² = (a+b)(a-b)