Multiple choice

If the equation of the form px² - qx + r = 0 has two roots whose roots are reciprocal to each other and are of same signs then which of following is true regarding p , q and r ?

  1. p > r

  2. p - r = 0

  3. p + r = 0

  4. p < r
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B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, if roots are reciprocals, the product of roots (c/a) = 1. Here, r/p = 1, so p = r, which means p - r = 0.

AI explanation

For a quadratic equation px^2 - qx + r = 0 with roots that are reciprocals of each other, the product of the roots is 1. The product of the roots is also given by the constant term divided by the leading coefficient, which equals r / p. Setting r / p = 1 means r = p, which can be rearranged as p - r = 0.

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