Question 986737: 1. What is the first thing you would do in order to use the quadratic formula to solve this equation?
x^2 + 7x = 9
2. In the following equation, what are the values of a, b, and c?
0 = 5x^2 + 3x - 19
3. Why/how does using the quadratic formula gives us two different roots (or solutions)?
4. Do ALL quadratic equations give us two roots (or solutions)? Explain your answer.
Thanks!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! make it the form of Ax^2+Bx+C=0
x^2+7x-9=0
no factors of 9 make 7.
Use quadratic formula
A=1
B=7
C=9
x=(1/2A) (-B +/- sqrt (B^2-4AC)
=(1/2)(-7+/- sqrt (49+36)); 4 (1)(-9) and you are subtracting this.
=(1/2)(-7+sqrt 85); (1/2) (-7-sqrt (85))
numerically, about (0.50(2.22) and (0.5)(16.22)
x=1.1, - 8.11 (approx)
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A=5
B=3
C=-19. They are the coefficients of the x^2, x , and constant respectively.
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Quadratic formula has a +/- square root term. That means there will be two answers, one by adding it to the rest of the equation, the other by subtracting it.
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They all have two roots BUT, a root may repeat, so there is only one root. This graphs "bounce" where it touches the x-axis in one place. Roots may also be complex (imaginary), so they do not cross the x-axis. These are important to realize. If one asks for roots of a quadratic equation, are complex roots considered? Are roots that repeat (x+2)^2=0 considered?
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