Multiple choice

Solve the following quadratic equation by factorization, the roots are : $5$, $\dfrac{-1}{3}$ $3x^2$ - 14x - 5 = 0

  1. True

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

For 3x^2 - 14x - 5 = 0, roots are x = [14 +/- sqrt(196 - 4*3*(-5))] / 6 = [14 +/- sqrt(256)] / 6 = [14 +/- 16] / 6. Roots are 30/6 = 5 and -2/6 = -1/3. The statement is True.

AI explanation

To factor 3x^2 - 14x - 5 = 0 by splitting the middle term, we write 3x^2 - 15x + x - 5 = 0. Factoring by grouping gives 3x(x - 5) + 1(x - 5) = 0, resulting in (3x + 1)(x - 5) = 0. Equating the factors to zero yields the roots 5 and -1/3, making the statement True.

Keep practicing — related questions