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If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of
If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
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Q1
If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
0
4
8
16
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For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0, leading to k = 4.
Questions & Step-by-step Solutions
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Q
Q: If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
Solution:
For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0, leading to k = 4.
Steps: 9
Show Steps
Step 1: Identify the quadratic equation given, 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 now we have D = 16 - 4k.
Step 6: For the roots to be equal, the discriminant must be zero. Set the equation to zero: 16 - 4k = 0.
Step 7: Solve for k by adding 4k to both sides: 16 = 4k.
Step 8: Divide both sides by 4 to isolate k: k = 16 / 4.
Step 9: Calculate 16 / 4, which equals 4. Therefore, k = 4.
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