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):
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:
The sign on the constant term is negative so the signs in the two binomial factors are opposite:
Now we need two integers whose product is -90 and whose sum is -1. How about -10 and 9?
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:
You can do your own arithmetic.
Graphing
Zeros of the quadratic function
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
