Algebra: Chapter 13, Lesson 4, page 589.
The Quadratic Formula, finally!
Given that `ax^2 + bx + c = 0`, then the quadratic formula
`x = (−b±sqrt(b^2−4ac))/(2a)`
gives the solutions of the quadratic equation. This requires that the quadratic equation is always in standard form:
- `a` is the coefficient of the `x^2` term
- `b` is the coefficient of the `x` term and
- `c` is the constant
Memorize it and memorize the discriminant, the expression under the radical (the `b^2−4ac` thingy).
- If the discriminant is > 0, then there are 2 real number solutions
- If the discriminant is = 0, then there is just 1 real number solution
- If the discriminant is < 0, then there are NO real number solutions because you don’t know (yet) how to take the root of a negative real number.
Don’t forget that the
- solutions
- answers
- x-intercepts
- roots and
- zeroes
all mean the same thing. By definition, the equation `ax^2+ bx + c=0` implies that we are setting `y = 0 ` and finding the x-intercepts or the roots or the answers or the solutions!!
Once again, Purplemath.com comes to the rescue, check out these examples for the use of the quadratic formula!