Solve the following quadratic equation using | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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: $2x^2 + ax - a^2 = 0$.

Similar Questions

The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

Find whether the following equation has real roots. If real roots exist,find them.
$8 x^{2}+2 x-3=0$

Examine whether the following equation is quadratic or not: $(2x + 1)(3x + 2) = 6(x - 1)(x - 2)$

If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

The value of the discriminant of the quadratic equation $x^{2}-8x+15=0$ is ...... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module