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For the quadratic equation x^2 + 4x + k = 0 to have real roots, what is the cond
For the quadratic equation x^2 + 4x + k = 0 to have real roots, what is the condition on k?
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Practice Questions
1 question
Q1
For the quadratic equation x^2 + 4x + k = 0 to have real roots, what is the condition on k?
k >= 4
k <= 4
k > 0
k < 0
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The discriminant must be non-negative: 4^2 - 4*1*k >= 0, which simplifies to k <= 4.
Questions & Step-by-step Solutions
1 item
Q
Q: For the quadratic equation x^2 + 4x + k = 0 to have real roots, what is the condition on k?
Solution:
The discriminant must be non-negative: 4^2 - 4*1*k >= 0, which simplifies to k <= 4.
Steps: 10
Show Steps
Step 1: Identify the quadratic equation, which is x^2 + 4x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant 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: Calculate 4^2, which is 16, so we have D = 16 - 4k.
Step 6: For the quadratic equation to have real roots, the discriminant must be non-negative: D >= 0.
Step 7: Set up the inequality: 16 - 4k >= 0.
Step 8: Rearrange the inequality to isolate k: 16 >= 4k.
Step 9: Divide both sides of the inequality by 4: 4 >= k.
Step 10: Rewrite the inequality: k <= 4.
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