Question

(ii)Find the quadratic polynomials whose zeros are 5 – 3 √2 and 5 + 3√2​

Answer 1

Answer :-

Quadratic polynomial = x² - 10x + 7

Step-by-step explanation :-

2 zeroes of a Quadratic polynomial are given and the question is about finding the polynomial.

Finding sum of zeros:

α + β = 5 - 3√2 + 5 + 3√2

⇒ α + β = 5 + 5

⇒ α + β = 10

Finding product of zeros:

αβ = (5 - 3√2) (5 + 3√2)

⇒ αβ = 5² - (3√2)²

⇒ αβ = 25 - 18

⇒ αβ = 7

Finding the polynomial:

Quadratic polynomial = x² - (α + β)x + αβ

⇒ Quadratic polynomial = x² - (10)x + 7

⇒ Quadratic polynomial = x² - 10x + 7

∴ Quadratic polynomial = x² - 10x + 7