Question

Find a quadratic polynomial with zeroes are 3 + √2 and 3 − √2.​

Answer 1

Answer:

Let the zeroes of the required polynomial be α and β.

∴ α = 3 + √2 β = 3 - √2

Now,

• Sum of zeroes, S = α + β

→ (3 + √2) + (3 - √2)

→ 3 + √2 + 3 - √2

→ 3 + 3

→ 6

• Product of zeroes, P = αβ

→ (3 + √2)(3 - √2)

• Identity : (a + b)(a - b) = a² - b²

Here, a = 3, b = √2

→ (3)² - (√2)²

→ 9 - 2

→ 7

The required polynomial is :

→ p(x) = k [x² - (S)x + (P)]

→ p(x) = k [x² - (6)x + (7)]

→ p(x) = k [x² - 6x + 7]

Putting the value of k = 1.

→ p(x) = x² - 6x + 7

Hence, the quadratic polynomial with zeroes (3 + √2) and (3 - √2) is x² - 6x + 7.