Easy way to find quadratic equations?

The quadratic formula ALWAYS works, but guessing at the factors is often faster.

Using the quadratic formula:

3y² - 4y - 7 = 0

y = [4 ± √(4² - 4(3)(-7))]/(2·3)

 = [4 ± √100]/6

 = [4 ± 10]/6

 = -1, 7/3

3y² - 4y - 7 = 3(y + 1)(y - 7/3)

     = (y + 1)(3y - 7)

If the coefficient of the squared term is 1, then guessing at factors is usually the fastest solution.

In your case, the coefficient is 3, not 1. That's when I go straight to the quadratic formula.

If you want to avoid that, here is a systematic way of guessing:

http://www.purplemath.com/modules/factquad2.htm

once you know the method if will be easy

(3)(– 7) = – 21

so there are 2 factors oe if greater and other is smaller

greater number will have – ve sign as middle tern is – ve

factors of 21 having difference 4

21

= 1 × 21 sum = 22 and difference = 20

= 3 × 7 sum = 10 but difference = 4 which is required.

so

3y^2 – 7y + 3y – 7 = 0

y(3y – 7) + 1(3y – 7) = 0

(y + 1)(3y – 7) = 0

y = – 1 or 7/3

----

( 3y - 7 ) ( y + 1 ) = 0

the quadratic formula is time consuming. That is why I avoid it unless it is absolutely necessary.

since the constant is a prime number with only two whole number factors (1,7) you might guess that (y+1) or (y-10 are factors, of course this might not prove to be true, but it's a goo place to start and can be checked quickly using "synthetic division"

if you are not familiar with syn. div. go to you tube and search "synthetic division" several videos will come up, the third down by patrickJMT is good - - syn. div. is a great tool leaving less chance for

errors and again proves or disproves your "guess" quickly.

Use the quadratic formula. It works on every quadratic equation.

x=(-b±sqrt(b²-4ac))/2a

Quadratic Equations should be in the form of ax²+bx+c=0 to use the formula.