Question

What does finding the discriminant of a quadratic equation help determine?

a) The number of solutions the equation possesses
b) The sum of the roots of the equation
c) The product of the roots of the equation
d) The equation's degree

Answer 1

The discriminant of a quadratic equation helps determine the number of solutions, sum of roots, and product of roots.

Step-by-step explanation:

The discriminant of a quadratic equation helps determine:

1. The number of solutions the equation possesses
2. The sum of the roots of the equation
3. The product of the roots of the equation

The discriminant is calculated using the formula:

Discriminant = b2 - 4ac

If the discriminant is:

• Positive, the equation has two real solutions.
• Zero, the equation has one real solution (a repeated root).
• Negative, the equation has no real solutions (two imaginary solutions).

Answer 2

Finding the discriminant of a quadratic equation helps determine (option a) the number of solutions the equation possesses.

Step-by-step explanation:

The discriminant, denoted by Δ, is a crucial component in quadratic equations of the form ax^2 + bx + c = 0. It is calculated as Δ = b^2 - 4ac. The value of the discriminant provides information about the nature of the roots of the quadratic equation. If Δ > 0, the equation has two distinct real roots; if Δ = 0, it has one real root (a repeated root); and if Δ < 0, the equation has two complex conjugate roots (option a).

For instance, consider the quadratic equation ax^2 + bx + c = 0. If the discriminant Δ is positive, it implies that there are two distinct real roots. If Δ is zero, there is one real root (a repeated root). If Δ is negative, it indicates two complex conjugate roots. Therefore, the discriminant is instrumental in determining the number and nature of solutions the quadratic equation possesses.

In summary, the discriminant is a valuable tool in analyzing quadratic equations, aiding in the identification of the type and quantity of roots the equation has. Its role is pivotal in understanding the behavior of quadratic equations and their solutions.