Question

Solve the quadratic equation 2x² + ax − a² = 0 for x.

Answer 1

We have:
2x² + ax − a² = 0
Comparing the given equation with the standard quadratic equation (ax² + bx + c = 0), we get:

a=2,b=a and c=-a²

Using the quadratic formula ,`x=(-b+-sqrt(b^2-4ac)/(2a))` , We get:

`x=-a+-sqrt(a^2-4xx2xx(-a^2))/(2xx2)`

`=(-a+sqrt(9a^2))4=(-a+3a)/4`

`=>x=(-a+3a)/4=a/2 or x=(-a-3a)/4=-a`

So, the solutions of the given quadratic equation are x=a/2 or x=-a