MATH 1090 Algebra and Trigonometry
Quiz 1 - Solutions

2002 Winter

Note: if you see symbols like ³ or Þ in various places, then the Symbol or WP MathA font is not installed on your computer. The translation is:

- = - (minus)	¹ = ¹ (not=)
Þ = Þ (implies)

Simplify the expression
[You may assume that x ¹ ±1 .]
$= [{(x-1)^2 + (x+1)^2} / {(x+1)(x-1)}] / [(1-x+x) / (1-x)]$ [common denominators]
$= [{(x^2-2x+1)+(x^2+2x+1)} / ((x+1)(x-1))] / [1 / (1-x)]$ [simplify numerators]

[cancellation permitted because we were given x ¹ 1]
Therefore the expression simplifies to

For the quadratic equation
x² - 6 x + 17 = 0
1. Use the discriminant to show that the solutions are not real.
  a = 1 , b = -6 , c = 17
  Þ D = b² - 4ac = 36 - 68 = -32
  D < 0 Þ the solutions are not real; [they are a complex conjugate pair].
2. Find the exact values, in simplified form, of these non-real solutions.
  
  Therefore the solutions are

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Dr. G.H. George