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If the quadratic equation x² - 4x + k = 0 has one real root, what must be the va
If the quadratic equation x² - 4x + k = 0 has one real root, what must be the value of k?
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Q1
If the quadratic equation x² - 4x + k = 0 has one real root, what must be the value of k?
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For the equation to have one real root, the discriminant must be zero. Thus, k must equal 4.
Questions & Step-by-step Solutions
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Q
Q: If the quadratic equation x² - 4x + k = 0 has one real root, what must be the value of k?
Solution:
For the equation to have one real root, the discriminant must be zero. Thus, k must equal 4.
Steps: 10
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Step 1: Identify the quadratic equation, which is x² - 4x + k = 0.
Step 2: Recall that a quadratic equation has one real root when its discriminant is zero.
Step 3: The discriminant (D) for a quadratic equation ax² + bx + c = 0 is given by the formula D = b² - 4ac.
Step 4: In our equation, a = 1, b = -4, and c = k.
Step 5: Substitute the values into the discriminant formula: D = (-4)² - 4(1)(k).
Step 6: Calculate (-4)², which is 16, so now we have D = 16 - 4k.
Step 7: Set the discriminant equal to zero for the equation to have one real root: 16 - 4k = 0.
Step 8: Solve for k by adding 4k to both sides: 16 = 4k.
Step 9: Divide both sides by 4 to isolate k: k = 16 / 4.
Step 10: Calculate 16 / 4, which equals 4. Therefore, k must be 4.
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