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# Math: discriminant, hw help?

### 1 Answer

- PuzzlingLv 74 months agoFavorite Answer
Think about the quadratic formula. The discriminant is that portion of the quadratic formula under the square root symbol, namely:

d = b² - 4ac

If the discriminant is negative (d < 0) then you are taking the square root of a negative and there will be 0 real roots.

If the discriminant is zero (d = 0) then you are taking the square root of zero then the ± sign in front will give you the same solution (because ± 0 doesn't change anything).

Finally, if the discriminant is positive (d > 0) then you have ± in front and you get two solutions.

Summary:

d = b² - 4ac

d < 0 means 0 real solutions

d = 0 means 1 real solution

d > 0 means 2 real solutions

In your particular quadratic:

a = 3

b = 24

c = 48

d = 24² - 4 * 3 * 48

d = 0

Answer:

The discriminant is zero, so you have 1 real root.

P.S. Please reread my reply in detail and let me know if there is *anything* I can clarify. Memorize the formula for the discriminant and then what it means.