Question

Solve by 'completion of square' or 'quadratic equation'

3. 2x^2 + ax - a^2 = 0

Ans: - a , a / 2

Standard:- 10

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Answer 1

Hey!!!!!

Good Evening

Difficulty Level : Above Average

Chances of being asked in Board : 80%

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We have

=> 2x² + ax - a² = 0

Divide both sides by 2

=> x² + ax/2 - a²/2 = 0

=> x² + ax/2 = a²/2

Add (a/4)² on both sides

=> x² + ax/2 + (a/4)² = a²/2 + a²/16


${(x + \frac{a}{4} )}^{2} = \frac{9 {a}^{2} }{16}$

Now
$= > x + \frac{a}{4} = + - \sqrt{ \frac{9 {a}^{2} }{16} }$

Thus now we have

=> x + a/4 = 3a/4 and x + a/4 = - 3a/4

Thus

=> x = a/2 or x = - a <<<<<<<< Answer

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Hope this helps ✌️

Good Night :-)

Answer 2

Heya!

Here is yr answer......


=> 2x² + ax - a² = 0

=> 2x² + 2ax - ax - a² = 0

=> 2x(x+a) - a(x+a) = 0

=> (x+a) (2x-a) = 0


x+a = 0 => x = -a

2x-a = 0 => x = a/2


Hope it hlpz u......