Question

If α and β are the zeroes of x2 + 7x + 10 then find (α/β) + (β/α).

Answer 1

Answer:-

Given quadratic equation is x² + 7x + 10.

Let,

• a = 1
• b = 7
• c = 10

We know that,

Sum of the zeroes = - b/a

⟶ α + β = - 7/1

⟶ α + β = - 7 -- equation (1)

Product of the zeroes = c/a

⟶ αβ = 10/1

⟶ αβ = 10 -- equation (2)

Now,

We have to find:

⟶ (α/β) + (β/α).

Taking LCM we get,

⟶ (α² + β²) / αβ

We know that,

(a + b)² = a² + b² + 2ab

→ (a + b)² - 2ab = a² + b²

⟶ ( α + β )² - 2αβ = α² + β²

Hence,

⟶ ( α + β )² - 2αβ / αβ

Putting the values from equations (1) & (2) we get,

⟶ [ ( - 7)² - 2(10) ] / 10

⟶ [ 49 - 20 ] / 10

⟶ 29/10

Hence, the value of α/β + β/α is 29/10.