If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the

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Question: If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following must be true? (2019)

Options:

Correct Answer: b^2 = 4ac

Exam Year: 2019

Solution:

For the roots to be equal, the discriminant must be zero, which means b^2 = 4ac.

If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following must be true? (2019)

If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following must be true? (2019)

Step 1: Understand what a quadratic equation is. It is in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Step 2: Identify what 'roots' of the equation mean. Roots are the values of x that make the equation true (i.e., where the equation equals zero).
Step 3: Learn about the discriminant. The discriminant is the part of the quadratic formula under the square root: b^2 - 4ac.
Step 4: Know that the roots of the quadratic equation are equal when the discriminant is zero.
Step 5: Set the discriminant equal to zero: b^2 - 4ac = 0.
Step 6: Rearrange the equation to find the condition for equal roots: b^2 = 4ac.

Discriminant of a Quadratic Equation – The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. The nature of the roots is determined by the value of D: if D > 0, the roots are real and distinct; if D = 0, the roots are real and equal; if D < 0, the roots are complex.