If the quadratic equation x^2 + 2x + k = 0 has equal roots, what is the value of

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

Options:

Correct Answer: -1

Solution:

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

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

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

Correct Answer: 1

Step 1: Identify the quadratic equation given, which is x^2 + 2x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant is calculated as D = b^2 - 4ac.
Step 3: In our equation, a = 1, b = 2, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = 2^2 - 4*1*k.
Step 5: Simplify the expression: D = 4 - 4k.
Step 6: For the roots to be equal, the discriminant must be zero. Set the discriminant equal to zero: 4 - 4k = 0.
Step 7: Solve for k by adding 4k to both sides: 4 = 4k.
Step 8: Divide both sides by 4 to isolate k: k = 1.

Discriminant of a Quadratic Equation – The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. For the equation to have equal roots, the discriminant must be zero.
Quadratic Equations – Quadratic equations are polynomial equations of degree 2, and their solutions can be found using the quadratic formula or by analyzing the discriminant.