Question

find the quadratic polynomial whose zeroes are in the ratio 2:3 and their sum is 15​

Answer 1

the quadratic polynomial will be

x2-15x+54

hope it will help you

Answer 2

Solution:

Let the zeroes of the polynomial be 2x and 3x respectively.

And α = 2x , β = 3x

Given that -

α + β = 15

⇒ 2x + 3x = 15

⇒ 5x = 15

⇒ x = 15 / 5

⇒ x = 3

Now,

α = 2x = 2 * 3 = 6

β = 3x = 3 * 3 = 9

So,

α + β = 15

αβ = 54

We know that, quadratic polynomial is given by -

⇒ x² - (α + β) x + αβ

⇒ x² - 15x + 54

Hence, the required quadratic polynomial is  x² - 15x + 54.