In the context of quadratic equations, which of the following statements is true

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Question: In the context of quadratic equations, which of the following statements is true?

Options:

Correct Answer: The roots of a quadratic equation can be both real and equal.

Solution:

The roots of a quadratic equation can be both real and equal when the discriminant is zero.

In the context of quadratic equations, which of the following statements is true?

In the context of quadratic equations, which of the following statements is true?

Step 1: Understand what a quadratic equation is. A quadratic equation is usually in the form of ax^2 + bx + c = 0, where a, b, and c are numbers and a is not zero.
Step 2: Learn about the roots of a quadratic equation. The roots are the values of x that make the equation true.
Step 3: Know what the discriminant is. The discriminant is the part of the quadratic formula under the square root, calculated as b^2 - 4ac.
Step 4: Determine the meaning of the discriminant. If the discriminant is greater than zero, there are two different real roots. If it is less than zero, there are no real roots. If it is exactly zero, there is one real root that is repeated (both roots are equal).
Step 5: Conclude that when the discriminant is zero, the roots of the quadratic equation are both real and equal.

Quadratic Equations – Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Discriminant – The discriminant of a quadratic equation, given by the formula D = b^2 - 4ac, determines the nature of the roots: if D > 0, roots are real and different; if D = 0, roots are real and equal; if D < 0, roots are complex.