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If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the mi
If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?
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Q1
If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?
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-4
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-16
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For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.
Questions & Step-by-step Solutions
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Q
Q: If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?
Solution:
For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.
Steps: 10
Show Steps
Step 1: Identify the equation given, which is x^2 + 4x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant (D) is given by the formula D = b^2 - 4ac.
Step 3: In our equation, a = 1, b = 4, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = 4^2 - 4(1)(k).
Step 5: Simplify the expression: D = 16 - 4k.
Step 6: For the roots to be real and equal, the discriminant must be equal to zero: 16 - 4k = 0.
Step 7: Solve the equation 16 - 4k = 0 for k.
Step 8: Rearrange the equation: 4k = 16.
Step 9: Divide both sides by 4: k = 4.
Step 10: Conclude that the minimum value of k for the roots to be real and equal is 4.
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