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

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Question: If the roots of the quadratic equation x^2 + 2x + k = 0 are equal, what is the value of k? (2022)

Options:

Correct Answer: -1

Exam Year: 2022

Solution:

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

If the roots of the quadratic equation x^2 + 2x + k = 0 are equal, what is the value of k? (2022)

If the roots of the quadratic equation x^2 + 2x + k = 0 are equal, what is the value of k? (2022)

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

Discriminant of a Quadratic Equation – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation. For equal roots, the discriminant must be zero.