How many distinct real solutions does the equation x^2 - 12x + 27 = 0 have?

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Multiple Choice

How many distinct real solutions does the equation x^2 - 12x + 27 = 0 have?

Explanation:
The number of real solutions for a quadratic is determined by the discriminant, b^2 − 4ac. For x^2 − 12x + 27 = 0, a = 1, b = −12, c = 27. The discriminant is (−12)^2 − 4(1)(27) = 144 − 108 = 36, which is positive. A positive discriminant means there are two distinct real solutions. Indeed, the equation factors as (x − 3)(x − 9) = 0, giving x = 3 and x = 9. So there are two real solutions.

The number of real solutions for a quadratic is determined by the discriminant, b^2 − 4ac. For x^2 − 12x + 27 = 0, a = 1, b = −12, c = 27. The discriminant is (−12)^2 − 4(1)(27) = 144 − 108 = 36, which is positive. A positive discriminant means there are two distinct real solutions. Indeed, the equation factors as (x − 3)(x − 9) = 0, giving x = 3 and x = 9. So there are two real solutions.

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