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JAMB Mathematics 1982 Question 8

Question 8

Graphs of Functions

The graphical method of solving the equation x3 + 3x2 + 4x − 28 = 0 is by drawing the graphs of the curves

  1. A.y = x3 and y = 3x2 + 4x − 28
  2. B.y = x3 + 3x2 + 4x − 28 and the line y = 1
  3. C.y = x3 + 3x2 + 4x and y = 28/x
  4. D.y = x2 + 3x + 4 and y = 28/x
  5. E.y = x2 + 3x + 4 and the line y = 28x.
Show the answer and explanation

Answer: D (y = x2 + 3x + 4 and y = 28/x)

Explanation

Rearranging gives x³ + 3x² + 4x = 28; dividing by x gives x² + 3x + 4 = 28/x. The solutions are where these two graphs cross.