Question

Find the quadratic polynomial whose zeros are
(5+2√3) and (5-2√3​

Answer 1

Answer :

• We are provided the zeros of the given quadratic polynomial that are (5 + 2 √3) and (5 - 2√3).

• And we need to find the quadratic polynomial.

Let the two zeros of the quadratic polynomial be as :

• a = (5 + 2 √3)
• b = (5 - 2√3)

◖S U M O F T H E Z E R O S :

↠Sum of zeros = a + b

↠Sum of zeros = (5 + 2 √3) + (5 - 2√3)

↠Sum of zeros = 5 + 5

↠Sum of zeros = 10

◖P R O D U C T O F T H E Z E R O S :

↠Product of zeros = a × b

↠Product of zeros = (5 + 2 √3) × (5 - 2√3)

↠Product of zeros = (5)² - (2√3)²

↠Product of zeros = 25 - (4 × 3)

↠Product of zeros = 25 - 12

↠Product of zeros = 13

◖Q U A D R A T I C P O L Y N O M I A L :

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

↠Quadratic polynomial = x² - (a + b)x + (ab)

↠Quadratic polynomial = x² - (10)x + (13)

↠Quadratic polynomial = x² - 10x + 13

∴ The required quadratic polynomial is x² - 10x + 13.

Answer 2

According to the question:

Let the two zeros of the quadratic polynomial be as :

• a = (5 +2√3)
• b = (5- 2√3)

Sum of the zeros:

Sum of zeros = a + b

Sum of zeros = (5 + 2√3) +(5-2√3)

Sum of zeros = 5 + 5

Sum of zeros = 10

Product of the zeros:

Product of zeros = a × b

Product of zeros = (5+2√3) ×(5-2√3)

Product of zeros = (5)^2 - (2√3)^2

Product of zeros = 25 - (4×3)

Product of zeros = 25 -12

Product of zeros = 13

Quadratic Polynomial :

Quadratic Polynomial = x^2 -(sum of zeros) +(product of zeros)

Quadratic Polynomial = x^2 - (a+b)x + (ab)

Quadratic Polynomial = x^2 -(10x ) + (13)

Quadratic Polynomial = x ^2 -10x + 13

The required quadratic Polynomial is x^2 -10x +13