Multiple choice

If the quadratic equation ${x^2} - 4x + 4p\left( {p - 1} \right) = 0$ possess roots of opposite sign then set values of p is

  1. (0,1)
  2. $\left( { - \infty ,0} \right)$

  3. (1,4)
  4. $\left( {1,\infty } \right)$
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A Correct answer
Explanation

For a quadratic equation to have roots of opposite signs, the product of the roots (c/a) must be negative. Here, 4p(p-1) < 0, which implies p(p-1) < 0. This inequality holds when p is between 0 and 1.

AI explanation

For a quadratic equation to have roots of opposite sign, its constant term must be less than zero by the condition of opposite signs. Setting 4p(p - 1) < 0 yields p(p - 1) < 0, which means p lies strictly between 0 and 1. The correct interval is (0, 1).

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