Multiple choice

Which one of the following equations does not have real roots?

  1. 2x2 + 16x + 3 = 0

  2. 2x2 + 10x - 1 = 0

  3. x2 - 8x + 1 = 0

  4. 4x2 + 9x + 6 = 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An equation has no real roots if the discriminant D = b^2 - 4ac < 0. For 4x^2 + 9x + 6 = 0, D = 9^2 - 4(4)(6) = 81 - 96 = -15, which is less than 0.

AI explanation

A quadratic equation does not have real roots when its discriminant is less than zero. For option D, the coefficients are a = 4, b = 9 and c = 6, giving a discriminant of 81 minus 96, which equals -15. Since this value is negative, the equation 4x2 + 9x + 6 = 0 does not have real roots.

Keep practicing — related questions