Question

Quadratic polynomial whose zeros are 2 +√3,2-√3

Answer 1

Answer:

Given zeroes of a quadratic polynomial:-

• 2 + √3
• 2 - √3

The quadractic polynomial when its zeros are given is :- x² - (Sum)x + Product.

Hence, x² - (2 + √3 + 2 - √3)x + (2 + √3)(2 - √3)

Solving,

x² - 4x + (4 - 2√3 + 2√3 - 3)

x² - 4x + 1 is the required quadratic polynomial.

SOME RULES –

• Sum of zeroes = -b/a
• Product of zeroes = c/a

• Quadractic polynomial has highest degree as 2.

• Three methods to find the series of a quadractic polynomial are -

1. Splitting the middle term
2. Quadractic Formula/Shreedhara charya formula
3. Completing the square method

Answer 2

Answer:

The Quadratic polynomial is x²-4x+1 .

Step-by-step explanation:

A quadratic polynomial has the highest degree as 2.

Quadratic polynomial f(x) =ax²-(sum) x+product.

Given zeros are 2+√3 and 2-√3.

Sum of the zeros = (2+√3+2-√3)

= 4

Product of the zeros = (2+√3)(2-√3)

= 4-3

= 1

Hence ,the required quadratic polynomial will be in the form x²-4x+1.