Multiple choice

If one root of the equation $px^2+qx+r=0$ is the reciprocal of the other, then

  1. $r=p$
  2. $p=q$
  3. $q=r$

  4. none of these
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A Correct answer
Explanation

If roots are reciprocals, their product is 1. For px^2 + qx + r = 0, the product of roots is r/p. Thus, r/p = 1, which means r = p.

AI explanation

Let the roots of the quadratic equation be alpha and 1 divided by alpha. The product of these roots is alpha times (1 divided by alpha), which equals 1. Using the formula for the product of roots of px squared plus qx plus r equals zero, the product is also equal to r divided by p. Equating the two expressions gives r divided by p equals 1, so r equals p.

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