Question

find the quadratic polynomial whose zeros are in the ratio 2 is to 3 and their sum is 15

Answer 1

Given :-

• Ratio of the zeroes of the quadratic polynomial= 2 : 3.
• Sum of the zeroes of the quadratic polynomial = 15.

To Find :-

• The required quadratic polynomial.

Solution :-

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

A.T.Q,

⇒ 2x + 3x = 15

⇒ 5x = 15

⇒ x = 15/5

⇒ x = 3

∴ Zeroes of the quadratic polynomial are,

⇒ 2 × 3 = 6 and,

⇒ 3 × 3 = 9

Then, the required polynomial,

⇒ x² - (sum)x + product

⇒ x² - (6 + 9) + 6 × 9

⇒ x² - 15x + 54

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