SOLUTION: Have to solve a Quadratic equation by Factoring as well as by using a quadratic formula. The quadratic formula has to show all steps and a final solution. Then l have to solve it b
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Question 456324: Have to solve a Quadratic equation by Factoring as well as by using a quadratic formula. The quadratic formula has to show all steps and a final solution. Then l have to solve it by the graphing method. The equation is x2-x-90. Hope you can help me
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is not an equation, quadratic or otherwise. Equations have to contain an equals sign and show that two things are equal to one another. A quadratic equation in standard form has a quadratic trinomial equal to zero. Presuming that is what you meant, namely:
Proceed as follows:
Factoring
The lead coefficient is 1, so:
(x\ \ \ )\ =\ 0)
The sign on the constant term is negative so the signs in the two binomial factors are opposite:
(x\ +\ )\ =\ 0)
Now we need two integers whose product is -90 and whose sum is -1. How about -10 and 9?
(x\ +\ 9)\ =\ 0)
Finally use the Zero Product Rule and set each of the binomials equal to 0 and solve each one to get the two roots you expect whenever you solve a quadratic.
Quadratic Formula
The quadratic formula is the general solution to the general quadratic equation:
namely:
In the case of:
, 
, and 
Just plug in the numbers and do the arithmetic:
\ \pm\ \sqrt{(-1)^2\ -\ 4(1)(-90)}}{2(-1)})
You can do your own arithmetic.
Graphing
Zeros of the quadratic function
\ =\ x^2\ -\ x\ -\ 90)
aka roots of the quadratic equation
are the 
-coordinates of the points where the graph of the function intersects the -axis, namely at )
and )
as we expected from our previous work.
John
My calculator said it, I believe it, that settles it
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