Question 693410: Finding finding the roots of a quadratic equation with leading coefficient greater than 1
Solve for u
3u^2-5u=2 Answer by pmatei(79) (Show Source):
You can put this solution on YOUR website! For quadratics you need everything on the left side of the equal sign:
There are 2 ways of solving quadratics.
A. You try to find to numbers that their product is equal to the product of the u^2 coefficient and the number without letter (in this case ), and their sum is equal to the u coefficient (in this case ). The numbers that multiplied give and added give are : and .
Instead of in the original equation write the two numbers multiplied by :
Group the four terms in 2 pairs: first two terms and last two terms.
See if you can factor out anything from those parentheses (you always have at least the letter from the first parenthesis):
If you done everything right the two parentheses are the same at this point. This repeated parenthesis is one of the 2 parentheses you want to solve the quadratic. The second one is put together by what you factored out:
For the quadratic solutions take each parenthesis and set it equal to zero.
First solution:
Second solution:
This method does not always work.
B. The second method is to know the quadratic formula, and works every time:
If then the solutions are given by:
In your case , , , .
First solution:
Second solution:
(