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For which value(s) of x does the determinant of the matrix | 1 (x−3) (x−3)^2 | | 1 (x−4) (x−4)^2 | | 1 (x−5) (x−5)^2 | become zero?

1. 3 values of x
2. 2 values of x
3. 1 value of x
4. no value of x

Correct answer: 1 value of x

Solution

The determinant of the given matrix is a polynomial in x, and it can be shown that it has a single root, indicating that it equals zero for only one specific value of x.

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