If the discriminant of a quadratic equation is 4, which statement describes the roots?
A. There are two complex roots.
B. There are two real roots.
C. There is one real root.
D. There is one complex root.

The discriminant of a quadratic equation is positive.
A positive discriminant indicates that the quadratic equation has two distinct real roots.
Therefore, the quadratic equation has two real roots.
The answer is: There are two real roots. ​

Explanation

Understanding the Discriminant The discriminant of a quadratic equation determines the nature of its roots. The discriminant, often denoted as Δ , is given by the formula Δ = b 2 − 4 a c for a quadratic equation of the form a x 2 + b x + c = 0 . The relationship between the discriminant and the roots is as follows:


If 0"> Δ > 0 , the equation has two distinct real roots.
If Δ = 0 , the equation has one real root (a repeated or double root).
If Δ < 0 , the equation has two complex conjugate roots.


Determining the Nature of Roots In this problem, the discriminant is given as 4, which is a positive number. Therefore, according to the rules above, the quadratic equation has two distinct real roots.

Conclusion Since the discriminant is positive (4 > 0), the quadratic equation has two distinct real roots.


Examples
Understanding the discriminant helps us predict the type of solutions we'll get when solving quadratic equations. For example, if we're designing a bridge and modeling its structure with a quadratic equation, knowing whether the roots are real or complex can tell us if our design is physically possible or if it requires adjustments. Similarly, in physics, when analyzing projectile motion, the discriminant can tell us whether a projectile will hit a target or not, based on the initial conditions.

Answered by GinnyAnswer | 2025-07-03

The discriminant is a key component in determining the nature of the roots of a quadratic equation. Since the discriminant is given as 4, which is positive, the quadratic equation has two distinct real roots. Hence, the correct answer is: B. There are two real roots.
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Answered by Anonymous | 2025-07-04