Multiple choice

Solve the following quadratic equation by factorization, the roots are $\dfrac{3b}{a}$, $-4a$ : $ax^2 \, + \, (4a^2 \, - \, 3b) \, x \, - \, 12ab \, = \, 0$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Expanding ax^2 + (4a^2 - 3b)x - 12ab = 0 gives ax^2 + 4a^2x - 3bx - 12ab = 0. Factoring: ax(x + 4a) - 3b(x + 4a) = 0, which is (ax - 3b)(x + 4a) = 0. The roots are x = 3b/a and x = -4a.

AI explanation

Split the middle term of ax^2 + (4a^2 - 3b)x - 12ab = 0 to get ax^2 + 4a^2x - 3bx - 12ab = 0. Factoring by grouping gives ax(x + 4a) - 3b(x + 4a) = 0, which yields (ax - 3b)(x + 4a) = 0. Setting the factors to zero gives the roots x = 3b/a and x = -4a. The statement is True.

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