How do you solve quadratic equation #4x^2+11x-20=0#?
The first method to check for solving a quadratic equation is whether the expression factorises.
"Find factors of 4 and 20 which subtract to make 11"
Note that 11 is ODD, so the factors must combine to give one ODD and and one even number.
That immediately eliminates
( because their multiples will always be even.)
When trying different combinations, remember not to have a common factor in any horizontal row.
Find factors and cross-multiply. Subtract the products to get 11.
We have the correct factors, now work with the signs.
Fill in the correct signs, starting from
Now fill in the signs next to the correct factors:
Now you have the factors: Top row is one bracket and bottom row is the other factor.
Letting each factor be equal to 0 gives the 2 solutions
Use the new Transforming Method (Socratic Search)
First, find the 2 real roots of y' that have opposite signs (ac < 0). Then, divide them by (a).
Factor pairs of (- 80) --> ...(4, - 20)(5, -16). This last sum is (-11 = -b). There for the 2 real roots of y' are: 5 and - 16.
The 2 real roots of y are: