Problem
45. The equation $x^{2}-2 x+36=0$ has how many roots? A no real roots B 1 real root C 2 real roots D 4 real roots
Solution
Step 1 ：Given the quadratic equation \(x^2 - 2x + 36 = 0\), we can use the discriminant to determine the number of real roots.
Step 2 ：The discriminant is given by the formula \(\Delta = b^2 - 4ac\).
Step 3 ：In this case, \(a = 1\), \(b = -2\), and \(c = 36\).
Step 4 ：Calculate the discriminant: \(\Delta = (-2)^2 - 4(1)(36) = 4 - 144 = -140\).
Step 5 ：Since the discriminant is negative, the equation has no real roots.
Step 6 ：Final Answer: \(\boxed{\text{A no real roots}}\)
