Question

Write the quadratic equation whose roots are 2+√3 and 2-√3

Answer 1

Answer:

x² - 4x + 1

Step-by-step explanation:

Given roots :

• 2 + √3
• 2 - √3

Sum of roots :

=> 2 + √3 + 2 - √3

=> 4

Product of roots :

=> (2+√3)(2-√3)

Using (a+b)(a-b) = a² - b²

=> 2² - (√3)²

=> 4 - 3

=> 1

Polynomial = x² - Sx + P

=> x² - 4x + 1

Answer 2

Answer:

x² - 4x + 1

Explaination:

Given:

(2 + √3) and (2 - √3) are the roots of the quadratic equation p(x)

To find: polynomial p(x)

Solution:

✰ Sum of the roots {α + β}

=> (2 + √3) + (2 - √3)

=> 2 + √3 + 2 - √3

=> 4

✰ Product of the roots {αβ}

=> (2 + √3) (2 - √3) ┃∵ (a+b) (a-b) = a² - b² ┃

=> (2)² - (√3)²

=> 4 - 3

=> 1

∴ The required polynomial = x² - (α + β)x + αβ

=> x² - 4x + 1