Question

If α and β are the roots of the equation ax² + bx + c = 0 then the value of 1/α² + 1/β² is:

 

1. (a² - 2cb)c²
2. (b2 – 2ca)/c2
3. (b2 + 2ca)/c2
4. (a² + 2bc)/c²

Answer 1

Correct Answer - Option 2 : (b2 – 2ca)/c2

Given:

Our given quadratic equation is ax2 + bx + c = 0  

Concept used:

General quadratic equation in terms of roots is x2 – (α + β)x + αβ = 0

Formula used:

a2 + b2 = (a + b)2 – 2ab

Calculation:

By comparing given quadratic equation with general quadratic equation, we get

(α + β) = –b/a and αβ = c/a

Now, 1/α2 + 1/β2

⇒ (α2 + β2)/(α2β2)

⇒ ((–b/a)2 – 2(c/a))/(c/a)2

⇒ (b2 – 2ca)/c2

∴ The required value of given expression is (b2 – 2ca)/c2