Multiple choice

The equation $x^2 - px + q = 0\ p, q \in R$ has no real roots if

  1. $p^2 > 4q$
  2. $p^2 < 4q$
  3. $p^2 = 4q$

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

A quadratic equation ax^2 + bx + c = 0 has no real roots if the discriminant b^2 - 4ac < 0. Here, a=1, b=-p, c=q. So (-p)^2 - 4(1)(q) < 0, which simplifies to p^2 < 4q.

AI explanation

The discriminant of a quadratic equation determines the nature of its roots, where the condition for no real roots is that the discriminant must be less than zero. For the equation x squared minus px plus q equals 0, the discriminant is p squared minus 4q, which must be less than zero. Rearranging this inequality gives p squared less than 4q.

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