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Question
`2x^2+ax-a^2=0`
Solution
The given equation is `2x^ax-a^2=0`
Comparing it with `Ax^2+bx+c=0`
`A=2,B=a and C=-a^2`
∴ Discriminant, `D= B^2-4AC=a^2-4xx2xxa^2=a^2+8a^2=9a^2≥0`
So, the given equation has real roots.
Now, `sqrtD=sqrt9a^2=3a`
`α=(-B+sqrtD)/(2A)=(-a+3a)/(2xx2)=(2a)/4=4/2`
`β=(-B+sqrtD)/(2A)=(-a+3a)/(2xx2)=(-4a)/4=-a`
Hence, `a/2` and `-a` are the roots of the given equation.
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