Multiple choice

The roots of the equation $x^2 - 2x = 0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:

  1. $ y = x^2, y = 2x$
  2. $y = x^2 - 2x, y =0$
  3. $y = x, y = x - 2$
  4. $y = x^2 - 2x + 1, y =1$
  5. $y = x^2 - 1, y =2x - 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The roots of x^2 - 2x = 0 are x = 0 and x = 2. Option C represents the system y = x and y = x - 2, which intersect at x = x - 2, implying 0 = -2, which is impossible. The other options represent systems that intersect at the correct roots.

AI explanation

The roots of x^2 - 2x = 0 are found where the two sides of the equation are equal. Setting the pair y = x and y = x - 2 equal gives x = x - 2, which simplifies to 0 = -2. Because this equation has no solution for x, this pair of equations cannot be used to find the roots graphically.

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