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Basics of Test Point Method

Basics of Test Point Method

TGM Original Questions
  1. Solve \(x(2-x)(x-3) > 0\).
  2. Solve \((x+5)(2x+1)(x-4) \le 0\).
  3. Solve \((x+5)(x+3)^2(x-4) \ge 0\).
  4. Solve \((3-2x)(2x-5)^2(x+1) \ge 0\).
  5. Solve \((3-x^2)(1-x)^2(x^2+2) > 0\).
  6. Solve \(x^2(5-x^2)(x^2 + x + 5) \le 0\).
  7. Solve \(\dfrac{(2x-5)(x-1)}{x(x+2)} \ge 0\).
  8. Solve \(\dfrac{(x+2)(3x+2)}{x(x-1)} \le 0\).
  9. Solve \(\dfrac{x^2+1}{x^2(x-1)} \ge 0\).
  10. Solve \(\dfrac{x-5-x^2}{(x^2+1)(x+2)} \le 0\).
  11. Solve \(\dfrac{(x+2)(3x+2)}{x(x-1)^2} \le 0\).
  12. Solve \(\dfrac{(1-x)(3x-5)}{x(x-1)^3} \ge 0\).

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Answer:(i) \(x<0\) or \(2 < x < 3\) (ii) \(x\leq -5\) or \(-\frac{1}{2}\leq x\leq 4\) (iii) \(x\leq -5\) or \(x=-3\) or \(x\geq 4\) (iv) \(-1\leq x\leq \frac{3}{2}\) or \(x=\frac{5}{2}\) (v) \( -\sqrt{3}< x <1 \) or \( 1 < x < \sqrt{3}\) (vi) \(x\leq -\sqrt{5}\) or \(x=0\) or \(x\geq \sqrt{5}\) (vii) \( x <-2\) or \(0 < x \leq 1\) or \(x\geq \frac{5}{2}\) (viii) \(-2\leq x < -\frac{2}{3}\) or \( 0 < x < 1\) (ix) \(x>1\) (x) \(x>-2\) (xi) \(x\leq -2\) or \(-\frac{2}{3}\leq x<0\) (xii) \(0 < x < 1\) or \(1 < x \leq \frac{5}{3}\)

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