If the roots of the equation x^2 + 2x + 1 = 0 are equal, what is the value of th

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Question: If the roots of the equation x^2 + 2x + 1 = 0 are equal, what is the value of the discriminant?

Options:

Correct Answer: 0

Solution:

The discriminant is given by b^2 - 4ac. Here, b = 2, a = 1, c = 1, so the discriminant is 2^2 - 4*1*1 = 0.

If the roots of the equation x^2 + 2x + 1 = 0 are equal, what is the value of the discriminant?

If the roots of the equation x^2 + 2x + 1 = 0 are equal, what is the value of the discriminant?

Step 1: Identify the equation given, which is x^2 + 2x + 1 = 0.
Step 2: Recognize that the equation is in the standard form ax^2 + bx + c, where a = 1, b = 2, and c = 1.
Step 3: Recall the formula for the discriminant, which is b^2 - 4ac.
Step 4: Substitute the values of a, b, and c into the discriminant formula: b^2 - 4ac = 2^2 - 4*1*1.
Step 5: Calculate 2^2, which is 4.
Step 6: Calculate 4*1*1, which is also 4.
Step 7: Now, subtract the two results: 4 - 4 = 0.
Step 8: Conclude that the value of the discriminant is 0.

Quadratic Equations – Understanding the properties of quadratic equations, specifically the condition for equal roots.
Discriminant – Calculating the discriminant to determine the nature of the roots of a quadratic equation.