Question

Find the quadratic polynomial is with the given numbers as the sum and the product of its zeros respectively question is root 2 ,1/3

Answer 1

Solution :

It is given that in a quadratic polynomial,

• Sum of zeroes $\sf = \sqrt{2}$
• Product of zeroes = 1/3

We've to find the quadratic polynomial.

As we know,

Quadratic Polynomial :

$\sf = k [ x^2 - (sum\:of\:zeroes)x + (product\:of\:zeroes)]$

Substitute the given values.

We get,

$\sf = k [ x^2 - (\sqrt{2})x + \dfrac{1}{2}]$

$\sf = k [ x^2 -\sqrt{2}x+\dfrac{1}{2}]$

In order to remove ' 2 ' from the denominator, let k = 2.

Now,

$\sf = 2[ x^2 - \sqrt{2}x + \dfrac{1}{2}]$

$\sf = 2x^2 - 2\sqrt{2}x + 1$

Hence,

the required quadratic polynomial is 2x² - 2√2x + 1.

$\rule{200}2$