Solve the quadratic equation 2x2+ax−a2=0 for x.
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,c=−a2
Using the quadratic formula, x=−b±√b2−4ac2a, we get :
x=−a±√a2−4×2×(−a)22×2
=−a±√9a24
=−a±3a4
⇒x=−a+3a4=a2 or x=a−3a4=−a
So, the solutions of the given quadratic equation are x=a2 or x=−a.