SOLUTION: For each of the following equations use the discriminant to determine what type of number the solutions will be (i.e. rational, irrational, or imaginary), and how many solutions ex

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Question 184704: For each of the following equations use the discriminant to determine what type of number the solutions will be (i.e. rational, irrational, or imaginary), and how many solutions exist. Defend your answers using algebra.

a) 9x^2-12x+4=0
b) 2x2+7x-3=0
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
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: 0.666666666666667, 0.666666666666667. Here's your graph:

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=73 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.386000936329383, -3.88600093632938. Here's your graph:
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