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## College Algebra

### Course: College Algebra>Unit 5

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations. Created by Sal Khan.

## Want to join the conversation?

• How difficult is it when you start using imaginary numbers?
• Don't let the term "imaginary" get in your way - there is nothing imaginary about them. They are just extensions of the real numbers, just like rational numbers (fractions) are an extension of the integers. Remember when you first started learning fractions, you encountered some different rules for adding, like the common denominator thing, as well as some other differences than the whole numbers you were used to. It seemed weird at the time, but now you are comfortable with them. Well, it is the same with imaginary numbers. They have some properties that are different from than the numbers you have been working with up to now - and that is it.

The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. The term "imaginary number" now means simply a complex number with a real part equal to 0, that is, a number of the form bi.

"What's that last bit, complex number and bi" you ask?!
You'll see when you get there. Meanwhile, try this to get your feet wet:
https://www.mathsisfun.com/numbers/imaginary-numbers.html

NOTE: The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. Really!
• i know how to do the quadratic formula, but my teacher gave me the problem ax squared + bx + c = 0 and she says a is not equal to zero, what are the solutions. i am not sure where to begin
• The solutions are just what the x values are! So you just take the quadratic equation and apply it to this. In Sal's completing the square vid, he takes the exact same equation (ax^2+bx+c = 0) and he completes the square, to end up isolating x and forming the equation into the quadratic formula. In other words, the quadratic formula is simply just ax^2+bx+c = 0 in terms of x. So the roots of ax^2+bx+c = 0 would just be the quadratic equation, which is:
(-b+-√b^2-4ac) / 2a. Hope this helped!
• I feel a little stupid, but how does he go from 100 to 10? , thanks a lot!
• The square root fo 100 = 10.
Square roots reverse an exponent of 2.
Since 10^2 = 100, then square root 100 = 10.
• At , how was he able to drop the 2 out of the equation?
Thanks!
• Sal skipped a couple of steps.
Factor out a GCF = 2: `[ 2 ( -6 +/- √39 )] / (-6)`
The common facgtor of 2 is then cancelled with the -6 to get: ` ( -6 +/- √39 ) / (-3)`

Hope this helps.
• I still do not know why this formula is important, so I'm having a hard time memorizing it.
• Some quadratic equations are not factorable and also would result in a mess of fractions if completing the square is used to solve them (example: 6x^2 + 7x - 8 = 0). The quadratic formula is most efficient for solving these more difficult quadratic equations.
Have a blessed, wonderful day!
• how to find the quadratic equation when the roots are given?
• Let's say that P(x) is a quadratic with roots x=a and x=b. This means that P(a)=P(b)=0. This is true if P(x) contains the factors (x - a) and (x - b), so we can write
P(x) = (x - a)(x - b).

Notice:
P(a) = (a - a)(a - b) = 0(a - b) = 0.
P(b) = (b - a)(b - b) = (b - a)0 = 0.

Since P(x) = (x - a)(x - b), we can expand this and obtain
P(x) = x² - bx - ax + ab = x² - (a + b)x + ab.
• if the "complete the square" method always works what is the point in remembering this formula?
• Completing the square can get messy. You will sometimes get a lot of fractions to work thru. In those situations, the quadratic formula is often easier.
• I just watched the video and I can hardly remember what it is, much less how to solve it. My head is spinning on trying to figure out what it all means and how it works. Can someone else explain how it works and what to do for the problems in a different way?