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Solve the quadratic equation 2x^2 + ax − a^2 = 0 for x. - Mathematics

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

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Solution

We have:
2x2 + axa2 = 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

Concept: Nature of Roots
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