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What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real
What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?
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Practice Questions
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Q1
What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?
-10
-5
5
10
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For one real root, the discriminant must be zero: k^2 - 4*1*25 = 0, thus k^2 = 100, giving k = -10 or k = 10.
Questions & Step-by-step Solutions
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Q
Q: What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?
Solution:
For one real root, the discriminant must be zero: k^2 - 4*1*25 = 0, thus k^2 = 100, giving k = -10 or k = 10.
Steps: 9
Show Steps
Step 1: Identify the quadratic equation, which is x^2 + kx + 25 = 0.
Step 2: Recall that a quadratic equation has one real root when its discriminant is zero.
Step 3: Write the formula for the discriminant, which is D = b^2 - 4ac. Here, a = 1, b = k, and c = 25.
Step 4: Substitute the values into the discriminant formula: D = k^2 - 4*1*25.
Step 5: Simplify the equation: D = k^2 - 100.
Step 6: Set the discriminant equal to zero for one real root: k^2 - 100 = 0.
Step 7: Solve for k by adding 100 to both sides: k^2 = 100.
Step 8: Take the square root of both sides: k = ±10.
Step 9: Conclude that the possible values for k are -10 and 10.
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