Multiple choice

For what value of m, the roots of the equation $x^2-x+m=0$ are non real?

  1. $(\dfrac{1}{4}, \infty )$
  2. $(-\infty, \dfrac{1}{4})$
  3. $(-\dfrac{1}{4}, \dfrac{1}{4})$

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

For a quadratic equation ax^2 + bx + c = 0 to have non-real roots, the discriminant D = b^2 - 4ac must be less than 0. Here, (-1)^2 - 4(1)(m) < 0, which simplifies to 1 - 4m < 0, or m > 1/4.

AI explanation

Using the discriminant condition, the roots are non-real when b^2 - 4ac < 0, so (-1)^2 - 4(1)(m) < 0 yields 1 - 4m < 0. Solving this inequality gives m > 1/4, which means the required interval is (1/4, infinity).

Keep practicing — related questions