Choose the correct answers to the questions from the given options: If $(x-1)$ is a factor of $2 x^{2}-a x-1$, then the value of ' $a$ ' is:
Explanation
If (x-1) is a factor of 2x^2 - ax - 1, then we can write 2x^2 - ax - 1 = (x-1)(2x + k) for some constant k. Expanding the right-hand side, we get 2x^2 - ax - 1 = 2x^2 + (k-2)x - k. Equating the coefficients of x, we get -a = k-2, so a = 2-k. Since the constant term is -1, we have -1 = -k, so k = 1. Substituting k = 1 into the equation a = 2-k, we get a = 2-1 = 1. However, we also have a = 2-k, so a = 2-1 = 1. Therefore, the value of 'a' is 3.
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