Question 860163: How do you solve these four problems im really lost
3V^2+9V-54=0
6X^2-2x-4=0
2X^2-7x-12=0
11K^2+8k+9=0
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How do you solve these four problems im really lost
3V^2+9V-54=0
Divide by 3, make it easier
v^2 + 3v - 18 = 0
Factor it
(v+6)*(v-3) = 0
Product = 0 --> 1 of the factors is zero
v+6 = 0
v = -6
---
v-3 = 0
v = +3
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6X^2-2x-4=0
Similar to #1
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2X^2-7x-12=0
Can't be factored, use the quadratic equation
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=145 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 4.76039864469807, -1.26039864469807.
Here's your graph:
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The solver always says it can be factored, ignore that.
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11K^2+8k+9=0
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation (in our case  ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant :  .
The discriminant -332 is less than zero. That means that there are no solutions among real numbers.
If you are a student of advanced school algebra and are aware about imaginary numbers, read on.
In the field of imaginary numbers, the square root of -332 is + or -  .
The solution is  , or
Here's your graph:
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