Question

alpha+beta=3,alpha and beta=2 find quadratic equation​

Answer 1

Given,

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

To Find,

• Quadratic polynomial.

According to the question,

We know that,

Quadratic polynomial,

⇢ x² - (Sum of roots)x + (Product of roots)

⇢ x² - (α + β)x + αβ

[ Put the values ]

⇢ x² - (3)x + 2

⇢ x² - 3x + 2

Therefore,

The quadratic polynomial is x² - 3x + 2.

For information,

• 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.