Question

> form a quadratic Polynomial
for which the sum and product of
zeroes are under root 2 and 1/3 respectively ​

Answer 1

Given:

• Sum of zeroes = √2
• Product of zeroes = 1/3

To find:

Quadratic polynomial = ?

Solution:

For answering such questions, we use the below formula

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

where

• (α + β) is the sum of zeroes
• αβ is the product of zeroes.

Now, substitute the given values in the equation.

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

$\Rightarrow \sf{Quadratic \: polynomial = x^{2} - (\sqrt{2})x+\dfrac{1}{3}}$

Multiply by 3 throughout the equation;

$\Rightarrow \sf{Quadratic \: polynomial = 3x^{2} - 3\sqrt{2}x + \not{3}\bigg(\dfrac{1}{\not{3}}\bigg) }$

So, we have

$\Rightarrow \boxed{\bf{Quadratic \: polynomial = 3x^{2} -3\sqrt{2}x+1}}$