Question

please say the ans friends​

Answer 1

★ Concept :-

To find the quadratic equation with roots we need to use formula

Quadratic polynomial = x² - (sum of roots)x + product of roots

a) Solution :-

Given , roots 3 + √5 , 3 - √5

We need to find the quadratic equation

Firstly finding sum of roots & product of roots

→ Sum of roots = 3 + √5 + 3 - √5 = 6

→ Product of roots = (3 + √5)(3 - √5) = 4

Now , substituting the values we have .

→ x² - 6x + 4

Hence , quadratic equation → x² - 6x + 4 = 0

b) Solution :-

Given , roots p +q , p - q

We need to find the quadratic equation

Firstly finding sum of roots & product of roots

→ Sum of roots = p + q + p - q = 2p

→ Product of roots = (p + q)(p - q) = p² - q²

Now , substituting the values we have

→ x² - 2px + (p² - q²)

Hence , quadratic polynomial → x² - 2px + (p² - q²) = 0