Question

Find the roots of the following equation, if they exist, by applying the quadratic formula:

2x² + ax – a² = 0

Answer 1

The given equation is 2x² + ax – a² = 0

Comparing it with ax² + bx + c = 0 

A = 2, B = a and C = –a² 

∴ Discriminant, D = B² – 4AC 

= a² – 4 × 2 × a²

= a² + 8a²

= 9a² ≥ 0 

So, the given equation has real roots.

Now, `sqrt(D) = sqrt(9)a^2 = 3a` 

`α = (-B + sqrt(D))/(2A)`

= `(-a + 3a)/(2 xx 2)`

= `(2a)/4`

= `4/2` 

`β = (-B + sqrt(D))/(2A)`

= `(-a + 3a)/(2 xx 2)`

= `(-4a)/4`

= –a 

Hence, `a/2` and `-a` are the roots of the given equation.