Question

hii, please solve this question and keep to me answer, plz... I will be thank full to u

Answer 1

Answer:

α + 2 = 4, β + 2 = 3

Step-by-step explanation:

Given Equation is x² - 3x + 2 = 0.

Here, a = 1, b = -3, c = 2

Given that α,β are roots of equation.

(i)

Sum of roots = -b/a

α + β = -(-3)/1

α + β = 3

α = 3 - β.

(ii)

Product of roots = c/a

αβ = 2

β = 2/α

Substitute (ii) in (i), we get

⇒ α = 3 - (2/α)

⇒ α² - 3α + 2 = 0

⇒ α² - 2α - α + 2 = 0

⇒ α(α - 2) - (α - 2) = 0

⇒ (α - 2)² = 0

⇒ α = 2.

Substitute α = 2 in (ii), we get

β = 2/α

β = 2/2

β = 1.

Hence:

α + 2 = 4.

β + 2 = 3.

Hope it helps!