SOLUTION: please help, -number of real solutions- 1.) -3x^2+9x-8=0 2.)8x^2-11x=-3 3.)x^2=-7x+7 4.)-4x^2-4=8x i have a test in ALG2 today please quick response thank you

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Question 547116: please help,
-number of real solutions-
1.) -3x^2+9x-8=0
2.)8x^2-11x=-3
3.)x^2=-7x+7
4.)-4x^2-4=8x
i have a test in ALG2 today please quick response thank you
Answer by JBarnum(2146)   (Show Source): You can put this solution on YOUR website!
1)
Solved by pluggable solver: SOLVE quadratic equation with variable
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 -15 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 -15 is + or - .

The solution is

Here's your graph:
no real number answers
2)
Solved by pluggable solver: SOLVE quadratic equation with variable
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=25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1, 0.375. Here's your graph:
2 answers
3)
Solved by pluggable solver: SOLVE quadratic equation with variable
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=77 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.887482193696061, -7.88748219369606. Here's your graph:
2 answers
4)
Solved by pluggable solver: SOLVE quadratic equation with variable
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=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: -1, -1. Here's your graph:
2 answers

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