Multiple choice

If $\alpha ,\beta $ are the roots of the equation ${x^2} + x + 1 = 0\,and\,\frac{\alpha }{\beta },\,\frac{\beta }{\alpha }$ are roots of the equation ${x^2} + px + q = 0$, then p equals

  1. -1

  2. 1

  3. -2

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Roots of x^2+x+1=0 are omega and omega^2. Roots of the new equation are omega/omega^2 = 1/omega = omega^2 and omega^2/omega = omega. The equation with roots omega and omega^2 is x^2+x+1=0. Thus p=1.

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