If a quadratic equation with real coefficients has a discriminant of 225, the what type of roots does it have?

rational

two real roots

if a quadratic equation with real coefficients has a discriminant of 225, then what type of roots does it have? rational, irrational or imaginary?

To determine the type of roots a quadratic equation with real coefficients has based on its discriminant, you need to analyze the value of the discriminant.

The discriminant is calculated using the following formula: Δ = b^2 - 4ac, where Δ is the discriminant, and a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, the discriminant is given as 225. So, we have Δ = 225.

Now, based on the value of the discriminant, there are three cases:

1. If Δ > 0: In this case, if the discriminant is positive, it means that there are two distinct real roots. Since 225 is greater than zero, the quadratic equation will have two real and distinct roots.

2. If Δ = 0: If the discriminant is zero, it means that the quadratic equation has only one real root. However, in this case, the discriminant is given as 225, which is not equal to zero. Therefore, this case does not apply.

3. If Δ < 0: If the discriminant is negative, it means that the quadratic equation has no real roots. However, in this case, the discriminant is given as 225, which is not less than zero. Therefore, this case does not apply either.

Since the discriminant (225) is greater than zero, it indicates that the quadratic equation has two real and distinct roots.

Imgainary

ijdghtfg

d