Question

In the trinomial 

Answer 1

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) ].