The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k?

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Question: The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)

Options:

Correct Answer: 9

Exam Year: 2020

Solution:

For equal roots, b^2 - 4ac = 0. Here, 6^2 - 4(1)(k) = 0, so k = 9.

The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)

The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)

Step 1: Identify the quadratic equation, which is x^2 + 6x + k = 0.
Step 2: Recognize that for a quadratic equation to have equal roots, the discriminant must be zero. The discriminant is given by the formula b^2 - 4ac.
Step 3: In our equation, a = 1, b = 6, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: 6^2 - 4(1)(k) = 0.
Step 5: Calculate 6^2, which is 36. So, we have 36 - 4k = 0.
Step 6: Rearrange the equation to solve for k: 36 = 4k.
Step 7: Divide both sides by 4 to find k: k = 36 / 4.
Step 8: Calculate 36 / 4, which equals 9. Therefore, k = 9.

Quadratic Equations – Understanding the conditions for equal roots in a quadratic equation, specifically using the discriminant.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation.