Question

The quadratic polynomial whose zeroes are 2and -3 is

Answer 1

Given : Zeroes of quadratic equation are 2 and -3.

To find : Quadratic equation

Solution :

Whenever we are given zeroes of equation and we are asked to find the quadratic equation, we use the concept of sum and product of zeroes.

Every quadratic equation is of the form,

• x² - ( sum of zeroes ) x +( product of zeroes )

So it is clear that to find the equation, firstly we have to find the product and sum of zeroes.

Let the zeroes be α = 2 and β = -3.

Sum of zeroes = α + β

Sum of zeroes = 2 + ( - 3 )

Sum of zeroes = 2 - 3

Sum of zeroes = - 1

Product of zeroes = α × β

Product of zeroes = 2 × ( -3)

Product of zeroes = -6

So the quadratic equation would be,

=> x² - ( sum ) x + Product

=> x² - ( -1 ) x + ( -6)

=> x² + x - 6

Hence the required quadratic equation is x² + x - 6 = 0.