Form a quadratic polynomial $p( x)$ with $3$ and $\frac{2}{5}$ as sum and product of its zeroes, respectively.

Given: A quadratic polynomial $p( x)$ with $3$ and $\frac{2}{5}$ as sum and product of its zeroes, respectively.

To do: To form the given quadratic polynomial.

Solution:

Let $\alpha$ and $\beta$ are the roots of the quadratic polynomial $p( x)$.

As given,  $\alpha+\beta=3\ .........\ ( i)$

$\alpha\beta=\frac{2}{5}\ ................\ ( ii)$

$\therefore$ The quadratic polynomial $p( x)=k( x^2-( \alpha+\beta)x+\alpha\beta$

$\Rightarrow p( x)=k( x^2-3x+\frac{2}{5})$

$\Rightarrow p( x)=k( 5x^2-15x+2)$

Thus, the quadratic polynomial is $p( x)=k( 5x^2-15x+2)$.

Tutorialspoint

e

Updated on: 10-Oct-2022

83 Views

Kickstart Your Career

Get certified by completing the course

Get Started