Multiple choice

If $-1,2$ and $\alpha$ are the roots of the equation $2{x}^{3}+{x}^{2}-7x-6=0$, then find $\alpha$.

  1. $-\dfrac32$
  2. $\dfrac32$
  3. $\dfrac12$
  4. $-\dfrac12$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cubic equation ax^3 + bx^2 + cx + d = 0, the product of roots is -d/a. Here, -1 * 2 * alpha = -(-6)/2 = 3. So -2 * alpha = 3, which means alpha = -3/2.

AI explanation

Using Vieta's formulas for a cubic equation ax^3 + bx^2 + cx + d = 0, the sum of its roots equals -b/a. For the equation 2x^3 + x^2 - 7x - 6 = 0, the sum of the roots -1, 2, and alpha is -1/2. Therefore, -1 + 2 + alpha = -1/2, which simplifies to 1 + alpha = -1/2. Solving this gives alpha = -3/2.

Keep practicing — related questions