Multiple choice

If p and q are non-zero constants the equation $\displaystyle x^{2}+px+q=0$ has roots$\displaystyle \alpha $ and $\displaystyle \beta $ the equation $\displaystyle qx^{2}+px+1=0$ has roots

  1. $\displaystyle \alpha $ and $\displaystyle \frac{1}{\beta }$
  2. $\displaystyle \frac{1}{\alpha }$ and $\displaystyle \beta $
  3. $\displaystyle \frac{1}{\alpha }$ and $\displaystyle \frac{1}{\beta }$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If x^2 + px + q = 0 has roots alpha and beta, then alpha * beta = q and alpha + beta = -p. For qx^2 + px + 1 = 0, the product of roots is 1/q = 1/(alpha * beta) and sum of roots is -p/q = (alpha + beta) / (alpha * beta) = 1/alpha + 1/beta. The roots are 1/alpha and 1/beta.

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