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If the quadratic equation x^2 + 2x + k = 0 has roots that are equal, what is the
If the quadratic equation x^2 + 2x + k = 0 has roots that are equal, what is the value of k?
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If the quadratic equation x^2 + 2x + k = 0 has roots that are equal, what is the value of k?
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For equal roots, the discriminant must be zero: 2^2 - 4*1*k = 0 leads to k = -1.
Questions & Step-by-step Solutions
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Q: If the quadratic equation x^2 + 2x + k = 0 has roots that are equal, what is the value of k?
Solution:
For equal roots, the discriminant must be zero: 2^2 - 4*1*k = 0 leads to k = -1.
Steps: 9
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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 (D) is calculated using the formula 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. So, set the equation to zero: 4 - 4k = 0.
Step 7: Solve for k by moving 4k to the other side: 4 = 4k.
Step 8: Divide both sides by 4 to isolate k: k = 1.
Step 9: Therefore, the value of k that makes the roots equal is k = 1.
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