Multiple choice

The value of $k$ such that the equation $\displaystyle x^{2}+\left ( k-1 \right )x+1=0$ has two equal roots

  1. $0$
  2. $-1$
  3. $1$
  4. $-10$
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B Correct answer
Explanation

For a quadratic equation to have equal roots, its discriminant must be equal to zero. Setting the discriminant (k-1)^2 - 4(1)(1) = 0 gives (k-1)^2 = 4, which means k-1 can be 2 or -2. This yields k = 3 or k = -1, and since -1 is among the choices, it is the correct answer.

AI explanation

A quadratic equation has two equal roots when its discriminant is zero. The discriminant is (k-1)^2 - 4(1)(1) = 0, which simplifies to k^2 - 2k - 3 = 0. Factoring this gives (k-3)(k+1) = 0, so k is 3 or -1. The value is -1.

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