Question

if α and β are zeroes of the polynomial x^2-3x+2, then find 1/α + 1/β

Answer 1

Given : α and β are the zeroes of the polynomial x² - 3x + 2

To find : 1/α + 1/β = ?

Solution > 1.

The given polynomial is x² - 3x + 2

Since α and β are the zeroes of the polynomial,

• α + β = - (- 3)/1 = 3
• αβ = 2/1 = 2

Now, 1/α + 1/β = (β + α)/(αβ) = 3/2

Solution > 2.

The given polynomial is x² - 3x + 2

= x² - 2x - x + 2

= x (x - 2) - 1 (x - 2)

= (x - 2) (x - 1)

The zeroes of the given polynomial be 2 and 1

Let, α = 2 and β = 1

Then, 1/α + 1/β = 1/ 2 + 1/1 = 1/2 + 1 = 3/2