For the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have? (2

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Question: For the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have? (2019)

Options:

Correct Answer: Real and equal

Exam Year: 2019

Solution:

The discriminant D = 6^2 - 4*1*9 = 0, indicating real and equal roots.

For the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have? (2019)

For the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have? (2019)

Step 1: Identify the coefficients in the quadratic equation x^2 + 6x + 9 = 0. Here, a = 1, b = 6, and c = 9.
Step 2: Use the formula for the discriminant D = b^2 - 4ac.
Step 3: Substitute the values of a, b, and c into the formula: D = 6^2 - 4*1*9.
Step 4: Calculate 6^2, which is 36.
Step 5: Calculate 4*1*9, which is 36.
Step 6: Now, subtract the two results: D = 36 - 36 = 0.
Step 7: Interpret the result: Since the discriminant D = 0, this means the quadratic equation has real and equal roots.

Quadratic Equation – A polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
Discriminant – A value calculated from the coefficients of a quadratic equation, given by D = b^2 - 4ac, which determines the nature of the roots.
Types of Roots – The roots of a quadratic equation can be real and distinct, real and equal, or complex, depending on the value of the discriminant.