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प्रश्न
Solve the following quadratic equations by factorization:
\[2x^2 + ax - a^2 = 0\]
Solve for x:
\[2x^2 + ax - a^2 = 0\]
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उत्तर
\[2 x^2 + ax - a^2 = 0\]
\[ \Rightarrow 2 x^2 + 2ax - ax - a^2 = 0\]
\[ \Rightarrow 2x\left( x + a \right) - a\left( x + a \right) = 0\]
\[ \Rightarrow \left( 2x - a \right)\left( x + a \right) = 0\]
\[ \Rightarrow 2x - a = 0 \text { or } x + a = 0\]
\[ \Rightarrow x = \frac{a}{2} \text { or } x = - a\]
Hence, the factors are \[\frac{a}{2}\] and \[- a\].
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