Quadratic Equation

What is a quadratic equation?

A quadratic equation is an equation that can be written in this form.

ax²+bx+c=0

The a,b, and c here represent real number coefficients. So this means we are talking about an equation that is a constant times the variable squared plus a constant times the variable plus a constant equals zero, where the coefficient a on the variable squared can't be zero, because if it were then it would be a linear equation.

Examples

2x²+3x+1=0, x²+x=2x+3, (x+2)(x+3)=5

All these equations are equivalent to equations of the above form. The first one is already in that form. The second one can be put into it by subtracting 2x+3 from both sides. The third one can be put into it by multiplying out and then subtracting 5 from both sides.

Standard Form

The form

ax²+bx+c=0

is the standard form for a quadratic equation, and for future reference, here the letter a will always mean the coefficient on the square of the variable, and b will be the coefficient on the variable, and c will be the constant term. To get a quadratic into standard form you must remove all parentheses and combine all like terms and add or subtract something from both sides so that the right side will be zero. Once you have your equation in standard form you can identify a,b, and c.