Question

find the required polynomial if sum of zeros are 2 + root 3 and product of zeros are 2 - root 3​

Answer 1

Answer:

Step-by-step explanation:

Given sum and products of roots are, 2+root3, 2-root3

Procedure

Required eqn of form : x^2-(sum of roots)+ product of roots

Answer

=x^2-( 2+root3) x+ (2-root3)

Answer 2

Answer:

Explanation:

Given :

• Sum of roots (α + β) = 2 + √3
• Product of roots (αβ) = 2 - √3

To Find :

• Required polynomial.

Solution :

We know,

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

=> Polynomial = x² - (2 + √3)x + 2 - √3

=> Polynomial = x² - 2x + √3x + 2 - √3

Hence :

The required polynomial is x² - 2x + √3x + 2 - √3.

Know to more :

• D < 0

• Nature of roots :- Roots are not real and unequal.

• D > 0

• Nature of roots :- Roots are real and unequal.

• D = 0

• Nature of roots :- Roots are real and equal.