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

Answer

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Answer

Final Answer: $\boxed{\text{A no real roots}}$

Steps

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: $\boxed{\text{A no real roots}}$