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(B) To solve the quadratic equation $2x^2 + ax - a^2 = 0$ by factorization,we need to split the middle term $ax$ into two parts such that their produc

Vedclass · Accepted Answer

$-a, \frac{a}{2}$

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(B) To solve the quadratic equation $2x^2 + ax - a^2 = 0$ by factorization,we need to split the middle term $ax$ into two parts such that their product is $(2x^2) 	imes (-a^2) = -2a^2x^2$ and their sum is $ax$.We can write $ax$ as $2ax - ax$.Substituting this into the equation: $2x^2 + 2ax - ax - a^2 = 0$.Grouping the terms: $2x(x + a) - a(x + a) = 0$.Factoring out the common term $(x + a)$: $(2x - a)(x + a) = 0$.Setting each factor to zero:$1$) $2x - a = 0 \implies 2x = a \implies x = \frac{a}{2}$.$2$) $x + a = 0 \implies x = -a$.Therefore,the solutions are $x = -a$ and $x = \frac{a}{2}$.

Solve the following quadratic equation using the method of factorization: $2x^2 + ax - a^2 = 0$.

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