Important Information About Solutions of Quadratic Equations

I am completely lost in this class. I really want to understand the concepts in this chapter. Can anyone help?

(1) How do you know if a quadratic equation will have one, two, or no solutions?

(2) How do you find a quadratic equation if you are only given the solution?

(3) Is it possible to have different quadratic equations with the same solution? Explain.

(4) Provide quadratic equations examples with one or two solutions with which they must create a quadratic equation.

Solution Preview

First off ... a quadratic equation is a polynomial that has an x^2 term (an x-squared term) but doesn't have an x^3, x^4, x^5 term or anything larger. A polynomial is an equation with whole number exponents for the x's. It is a "normal looking" equation -- it doesn't have anything that looks like a square root and doesn't have any x's on the bottom of fractions.

If you graph a quadratic equation, it looks like a parabola. It opens up if the x^2 is multiplied by a positive number and opens down if it's multiplied by a negative number.

A solution to the quadratic equation is a number(s) so that if you make x equal that number (or numbers), y equals 0. You can also think of it as the point where the parabola crosses the x-axis.

(1) ...

Solution Summary

The solution defines the terms "quadratic equation", "polynomial", and "solution". It then answers all four questions using examples to clarify the concepts.

Write a quadratic equation (see attachment)
How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only give the solution? Is it possible to have different quadraticequations with the same solution? Explain. Provide your classmate's with one or two solutio

1. Read Ch. 11 (attached)of Introductory and Intermediate Algebra.
· Post a response to the following: How do you know if a quadratic equation will have one, two, or
no solutions? How do you find a quadratic equation if you are only given the solution? Is it
possible to have different quadraticequations with the same solut

Determine the number and types of solutions for the following
quadraticequations
x2 - 5x = -6
Determine the value of c for which the following quadraticequations
will have one root.
(see attachment for the rest)

1. Determine whether the following equations have a solution or not? Justify your answer.
a) x^2+6x-7=0
b) z^2+z+1=0
c) (3)^1/2y^2-4y-7(3)^1/2=0
d) 2x^2-10x+25=0
e) 2x^2-6x+5=0
f) s^2-4s+4=0
g) 5/6x^2-7x-6/5=0
h) 7a^2+8a+2=0
2. If x=1 and x=-8, then form a quadratic equation.
3. What type of solution do

1. Determine whether the following equations have a solution or not? Justify your answer.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3x2 - 2x + 3/4 = 0
e) 2x2 + 5x + 5 = 0
f) p2 - 4p + 4 = 0
g) m2 + m + 1 = 0
h) 3z2 + z - 1 = 0
2. If x = 3 and x = -5, then form a quadratic equat

A. Why do you factor a quadratic equation before you solve?
B. Why are there usually two solutions in quadraticequations? Under what conditions will a quadratic equation have only one solution? No solutions?
C. How can you tell before solving the equation how many solutions to expect?

1) I am trying to solve the following quadraticequations that I have been studying for a test.
a) x^2+7x+10=0
b) 2x^2-3x-2=0
2) Compute the discriminant of the quadratic equation 3x^2+x+2=0, then write a brief sentence describing the number and type of solutions for this equation.