Please write "x^2" or "x squared," but not "x square2"
Given 1x^2 + bx + c, where b and c are negative, we could first find the two roots and then write out the factors based upon the roots.
Let's see what the quadratic formula can do for us:
a=1, b=a negative number, and c = also a negative number
According to the quadratic formula, the two roots are:
-b plus or minus sqrt(b^2 - 4ac)
x = --------------------------------------------
2(1)
Note well: If b is neg, then b^2 is positive, and -b is also positive.
The determinant b^2 - 4ac will be positive, since the negative property of c results in (positive number) - 4(1)(negative number),
which simplifies to (positive number) + positive number, or
b^2 + sqrt(positive number)
Because of this, we can predict that the quadratic equation will have two real, unequal roots.
Suppose one root is a and the other is b. Then the factors of the quadratic are:
(x-a) and (x-b).
Suppose that the root a is 1 + sqrt (b^2 - 4ac) has been found and is real.
The corresponding factor would then be (x - [1 + sqrt(b^2-4ac) ].
