If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the
Practice Questions
Q1
If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c?
b^2 - 4ac > 0
b^2 - 4ac = 0
b^2 - 4ac < 0
a + b + c = 0
Questions & Step-by-Step Solutions
If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c?
Correct Answer: b^2 - 4ac = 0
Step 1: Understand that a quadratic equation is in the form ax^2 + bx + c = 0.
Step 2: Recognize that the roots of the equation are the values of x that make the equation true.
Step 3: Know that the roots can be equal if the graph of the equation touches the x-axis at one point.
Step 4: The condition for this to happen is related to the discriminant, which is calculated as b^2 - 4ac.
Step 5: For the roots to be equal, the discriminant must be equal to zero: b^2 - 4ac = 0.
Discriminant of a Quadratic Equation – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation. If it equals zero, the roots are equal.
