Question

Find the quadratic polynomial whose zeroes are 5over 2 and -5over2

Answer 1

Answer:  The required quadratic polynomial is $4x^2-25=0.$

Step-by-step explanation:  We are given to find the quadratic polynomial with the following two zeroes :

$\dfrac{5}{2}~~~\textup{and}~~~-\dfrac{5}{2}.$

We know that

a quadratic polynomial with a and b as its two zeroes can be written as follows :

$x^2-(a+b)+ab=0.$

For the given polynomial, we have

$a=\dfrac{5}{2},~~~b=-\dfrac{5}{2}.$

Therefore, the quadratic polynomial is given by

$x^2-(a+b)x+ab=0\\\\\\\Rightarrow x^2-\left(\dfrac{5}{2}+\left(-\dfrac{5}{2}\right)\right)x+\dfrac{5}{2}\times\left(-\dfrac{5}{2}\right)=0\\\\\\\Rightarrow x^2-\left(\dfrac{5}{2}-\dfrac{5}{2}\right)-\dfrac{25}{4}=0\\\\\\\Rightarrow x^2-0\timesx-\dfrac{25}{4}=0\\\\\\\Rightarrow x^2-\dfrac{25}{4}=0\\\\\Rightarrow 4x^2-25=0.$

Thus, the required quadratic polynomial is $4x^2-25=0.$