Solve the following quadratic equation using quadratic formula: $3a^2x^2+abx-2b^2=0$
- $\left \{ \dfrac{2b}{3a},- \dfrac{b}{a} \right \}$
- $\left \{ \dfrac{2b}{3a}, \dfrac{b}{a} \right \}$
- $\left \{ -\dfrac{2b}{3a}, \dfrac{-b}{a} \right \}$
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None of these
Reveal answer
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A
Correct answer
Explanation
3a^2x^2 + abx - 2b^2 = 0. Using quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a. x = (-ab +/- sqrt((ab)^2 - 4(3a^2)(-2b^2))) / (2*3a^2). x = (-ab +/- sqrt(a^2b^2 + 24a^2b^2)) / 6a^2. x = (-ab +/- sqrt(25a^2b^2)) / 6a^2. x = (-ab +/- 5ab) / 6a^2. Roots: (4ab)/6a^2 = 2b/3a and (-6ab)/6a^2 = -b/a.
AI explanation
For the equation 3a^2x^2 + abx - 2b^2 = 0, the quadratic formula gives a discriminant of (ab)^2 - 4(3a^2)(-2b^2), which equals a^2b^2 + 24a^2b^2 or 25a^2b^2. The solutions for x are (-ab +/- 5ab) / 6a^2. Calculating the positive root gives 4ab / 6a^2 = 2b / 3a, and the negative root gives -6ab / 6a^2 = -b/a.