In the context of quadratic equations, which of the following statements is true?
Practice Questions
1 question
Q1
In the context of quadratic equations, which of the following statements is true?
The roots of a quadratic equation can be both real and equal.
A quadratic equation can have more than two roots.
The graph of a quadratic equation is a straight line.
The discriminant of a quadratic equation is always positive.
The roots of a quadratic equation can be both real and equal when the discriminant is zero.
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of quadratic equations, which of the following statements is true?
Solution: The roots of a quadratic equation can be both real and equal when the discriminant is zero.
Steps: 5
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.
