Multiple choice

3x2 + bx + 5 = 0 For the quadratic equation shown, b is a constant. If the equation has no real solutions, which of the following must be true?

  1. b2 < 60

  2. b2 > 60

  3. b < 0

  4. b > 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For no real solutions, the discriminant D = b^2 - 4ac must be less than 0. Here a=3, c=5. D = b^2 - 4(3)(5) = b^2 - 60. So b^2 - 60 < 0, which means b^2 < 60.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to have no real solutions, the discriminant (b^2 - 4ac) must be strictly less than zero. Substituting the given values into the discriminant formula gives b^2 - 4(3)(5) < 0, which simplifies to b^2 - 60 < 0. This inequality shows that b^2 must be less than 60.

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