Question

Find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2.​

Answer 1

Answer:

The quadratic polynomial whose zeroes are 5-3√2 and 5+3√2 is x² - 10x + 7.

Step-by-step-explanation:

Sum of the zeroes = ?

⟹ (5-3√2) + (5+3√2)

⟹ 5-3√2 + 5+3√2

⟹ 5 + 5

⟹ 10

∴ Sum of the zeroes is 10.

Now,

Product of zeroes = ?

⟹ (5-3√2) × (5+3√2)

⟹ 5² - (3√2)²

⟹ 25 - 9 × 2

⟹ 25 - 18

⟹ 7

∴ Product of zeroes is 7.

The required polynominal,

P(x) = x² - (Sum of zeroes)x + product of zeroes.

⟹ x² - 10x + 7

∴ The quadratic polynomial whose zeroes are 5-3√2 and 5+3√2 is x² - 10x + 7.