What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?
Correct Answer: 10 or -10
- 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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