MAT 117 /MAT117 Week 7 Discussion Question
Week 7 DQ 1
1. Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions?
2. Explain why.
3. Provide an example for your classmates where they have to figure out how many solutions a quadratic has.
Quadratic equations have the form, ax2 + bx + c = 0, where a, b, and c are numbers and x is a variable. Since the given polynomial has degree of 2 (or the highest exponent of x), it will either have 0, 1, 2, or infinitely many solutions.
There are only infinitely many solutions when a, b, and c are all equal to zero. Otherwise, the number of solutions can be found by examining the discriminant.The discriminant provides information about the number of solutions there are to a quadratic equation, and is the quantity b2 – 4ac. If the discriminant b2 – 4ac > 0, then there are two real solutions.
If the discriminant b2 – 4ac = 0, this tells us that there is one real solution.
If the discriminant b2 – 4ac < 0,there will be no real solutions, but that there are two complex solutions.
Solve the following example and find how many solutions the given quadratic has:
2x2 + 5x + 2
A quadratic equation will have zero, one, or two, amount of solutions if "a" does not equal zero. Since a quadratic equation has a "U" shape when graphed, you can assume that it will cross the x axis, once, twice, or not at all! This means that a quadratic equation equals zero when it hits the x axis at y=0. So, the equation can be plotted out and graphed, but may not have any "solutions."
One way to always solve a quadratic equation is with the quadratic formula where;
x= (-b)±sqrt(b²-4ac) 2a
This would allow you to find one positive or negative solution, two positive or negative solutions, one positive and negative solution, or no real number with no solution.
A quadratic equation for the class to solve is;
After reading the text for this week, I learned a lot about quadratic equations. Quadratic equations, which are written in the form of ax2 + bx + c = 0, where a does not equal 0. Since the quadratic equation has degree of 2 (the highest exponent) it can have 0, 1, 2, or infinitely many solutions.
The best way to figure out how many solutions an equation has is to factor it out. If A, B, and C are all equal to zero then the equation has infinitely many solutions. otherwise, we can find the number of solutions by examining the discriminant, which in this case is the quantity b2 - 4ac. If the discriminant is negative, there are no (real) solutions. If the discriminant equals zero, we have what is called a "repeated root" and there is exactly one (real) solution. Otherwise, if the discriminant is positive, there are two distinct (real) solutions.
An example for the class is 3x² + 10x + 8
A quadratic equation is expressed in the form ax²+bx+c=0 where a does not equal zero. The quadratic equation can have zero, one, or two solutions. When given a quadratic equation you start to solve it and see how many solutions you can come up with. It depends on the equation given as to how many solutions may be found. You can check your solutions by graphing them and seeing how many times the lines cross the x-axis. The y has to equal zero and that shows the solutions. The graph can be a right side up U or an upside down U. It can cross zero, one, or two times.
For example x²+2=0 has no solutions x²=-2 x² is less than zero and will not work.
x²=9 has one solution
The square root of x² = x. The square root of 9 = 3. x=3 x²-12x+35=0 has two solutions
Example for the class:
x²-5x-50=0 How many solutions?
A quadratic equation has either 1, 2 or no real