Multiple choice

State the whether given statement is true or false The given quadratic equations have real roots $3a^2x^2 \, + \, 8abx \, + \, 4b^2 \, = \, 0, \, a ,b\, \neq \, 0$

  1. True

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

The discriminant D = (8ab)^2 - 4(3a^2)(4b^2) = 64a^2b^2 - 48a^2b^2 = 16a^2b^2. Since a, b are not 0, D > 0, so the roots are real and distinct.

AI explanation

For the quadratic equation 3a^2x^2 + 8abx + 4b^2 = 0, split the middle term to get 3a^2x^2 + 6abx + 2abx + 4b^2 = 0. Factoring by grouping gives 3ax(ax + 2b) + 2b(ax + 2b) = 0, resulting in factors (3ax + 2b)(ax + 2b) = 0. Since the factors easily produce real roots, the equation has real roots. The statement is True.

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