Question

37. Form a quadratic polynomial whose zeroes are 7+ √5 and 7-√5.​

Answer 1

Answer: x² - 14x + 44

Given:

• Zeroes of polynomial = (7 + √5), (7 - √5)

To find:

Quadratic polynomial = ?

Solution:

First, find out the sum of zeroes and the product of zeroes of a given polynomial.

  Sum of zeroes = α + β

where

α and β are roots of the polynomial

   Sum of zeroes = α + β

⇒ Sum of zeroes = (7 + √5) + (7 - √5)

⇒ Sum of zeroes = 7 + √5 + 7 - √5

∴ Sum of zeroes = 14

   Product of zeroes = αβ

⇒ Product of zeroes = (7 + √5) (7 - √5)

⇒ Product of zeroes = (7)² - (√5)²

⇒ Product of zeroes = 49 - 5

∴ Product of zeroes = 44

For solving such types of questions, apply the below formula.

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

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

➥ Quadratic polynomial = x² - (14)x + 44

∴ Required quadratic polynomial → x² - 14x + 44