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When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

• a ratio is the comparison of two numbers that can be expressed as quotient $$a:b = \frac{a}{b}$$

Ratios, rates, proportion and odds

• ratios
  
  • a ratio is the comparison of two numbers that can be expressed as quotient $$a:b \rightarrow \frac{a}{b}$$
  • rate
    
    • a rate is a type of ratio, expressed as a quotient, comparing the change in one value (numerator) per change in another value (denominator): $$\Delta a:\Delta b \rightarrow \frac{\Delta a}{\Delta b} $$
    • example: death rate, calculate as the number of deaths divided by the person time at risk
  • proportion
    
    • a proportion is a type of ratio, expressed as a quotient, comparing a part (numerator) to the whole (denominator): $$ a:(a+b) \rightarrow \frac{a}{a+b}$$
  • odds
    
    • is a type of ratio, expressed as quotient, comparing a part (numerator) to the remainder (denominator): $$c:d \rightarrow \frac{c}{d}$$