Multiple choice

If $\alpha $ and $\beta $ are the zeros of the quadratic polynomial $f(x) =x^2- x -2$, find the value of $\frac{1}{\alpha}-\frac{1}{\beta}.$

  1. $\dfrac{-3}{2}$
  2. $\dfrac{1}{2} $
  3. $\dfrac{3}{2}$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For x^2 - x - 2, roots are (x-2)(x+1)=0, so 2 and -1. 1/alpha - 1/beta = (beta - alpha) / (alpha * beta). alpha + beta = 1, alpha * beta = -2. (beta - alpha)^2 = (alpha + beta)^2 - 4 * alpha * beta = 1 - 4(-2) = 9. beta - alpha = 3 or -3. Result = 3 / -2 = -1.5 or 1.5. Option C is 3/2.

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