If the roots of the equation x^2 + 3x + k = 0 are equal, what is the value of k?

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Question: If the roots of the equation x^2 + 3x + k = 0 are equal, what is the value of k?

Options:

Correct Answer: -9

Solution:

For equal roots, the discriminant must be zero: 3^2 - 4*1*k = 0, hence k = 9.

If the roots of the equation x^2 + 3x + k = 0 are equal, what is the value of k?

If the roots of the equation x^2 + 3x + k = 0 are equal, what is the value of k?

Step 1: Identify the equation given, which is x^2 + 3x + k = 0.
Step 2: Understand that for a quadratic equation to have equal roots, the discriminant must be zero.
Step 3: The discriminant formula for a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac.
Step 4: In our equation, a = 1, b = 3, and c = k.
Step 5: Substitute the values into the discriminant formula: D = 3^2 - 4*1*k.
Step 6: Simplify the expression: D = 9 - 4k.
Step 7: Set the discriminant equal to zero for equal roots: 9 - 4k = 0.
Step 8: Solve for k by rearranging the equation: 4k = 9.
Step 9: Divide both sides by 4 to find k: k = 9/4.
Step 10: Conclude that the value of k is 9/4.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots; for equal roots, it must be zero.
Quadratic Equation – A polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.