Multiple choice

One of the roots of the equation x2 − 4x + k = 0 is x = 3. The other root is:

  1. x = −1

  2. x = −4

  3. x = 4

  4. x = 1
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D Correct answer
Explanation

For the equation x^2 - 4x + k = 0, the sum of the roots is equal to -(-4)/1 = 4. If one root is 3, let the other be r. Then 3 + r = 4, which means r = 1.

AI explanation

Using Vieta's formulas for the quadratic equation x^2 - 4x + k = 0, the sum of the roots equals the negative of the coefficient of x divided by the coefficient of x^2, giving 3 + x2 = 4. Solving this equation gives the other root as x = 1.

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