Question

What does "quadratic equation" mean and how can you differentiate a quadratic equation from other equations

Answer 1

A quadratic equation with one variable has the form

         $ax^2+bx+c=0$

with a, b, c real numbers.

The variable can only be affected by exponents 1 and 2. For example, it can't be affected by:

• Other exponents: $x^3$, $(2x-5)^7$, $x^{2/3}$

• Roots: $\sqrt{x}$, $\sqrt[3]{x+2}$

• Denominator of a fraction: $\frac{2}{x},\;\frac{1}{x^2+9}$

• Logarithms: $\log x,\;\log_2 (x-1)$
• Trigonometric functions: $\sin x,\;\cos(x+4)$
• Exponentials: $e^x,\;2^{x+3}$