Question

The discriminant of a quadratic equation is 40. What is the nature of solutions?

Answer 1

The quadratic equation with a discriminant of 40 will have two distinct real solutions because the positive discriminant indicates that the solutions are not repeated or complex.

Step-by-step explanation:

The discriminant of a quadratic equation provides information about the nature of its solutions. Given that the discriminant is 40, which is a positive number, the quadratic equation will have two distinct real solutions. This is because the value of the discriminant (Δ=b²-4ac) informs us whether the solutions are real and distinct, real and identical, or complex.

Looking at an example of a quadratic equation at² + bt + c = 0, we can apply the known values for a, b, and c (α = 4.90, β = 14.3, γ = -20.0), and even without calculating the discriminant explicitly, any positive discriminant would indicate two real solutions.

The Solution of Quadratic Equations using the quadratic formula, x = ± [√(b²-4ac) - b] / (2a), can now be pursued, assured that the solutions will be real numbers.

Answer 2

It means that the roots of the quadratic equation are real and distinct

Step-by-step explanation:

Here, given the discriminant of the quadratic equation, we want to find out the nature of the solutions.

Mathematically, we can use to determine the nature of the discriminant.

By it’s formula;

D = b^2 - 4ac

We can see that the given discriminant 40 is a positive value. What this means is that the quadratic equation has roots which are real and are distinct