# Why can there only be 0 to 2 answers to a quadratic equation?

• Mar 28th 2008, 04:01 PM
phillychum
Why can there only be 0 to 2 answers to a quadratic equation?
This is one of the questions in my maths assignment which is due in a few days !.. It says.. "Why can there only be 0 to 2 answers to a quadratic equation? (Use mathematical terminology)."

We never did quadratic equations into detail at school. I guess the teacher wants us to research ourselves, but i can't find anything about why.
• Mar 28th 2008, 04:10 PM
topsquark
Quote:

Originally Posted by phillychum
This is one of the questions in my maths assignment which is due in a few days !.. It says.. "Why can there only be 0 to 2 answers to a quadratic equation? (Use mathematical terminology)."

We never did quadratic equations into detail at school. I guess the teacher wants us to research ourselves, but i can't find anything about why.

The quadratic equation is a second degree equation. It forms parabolas. What is the general shape of a parabola? How does this help you answer the question?

I beg to differ in one sense though. \$\displaystyle x^2 - 1 = 0\$ has only one solution. (Though you can call it "two real identical" solutions for technical reasons.)

-Dan
• Mar 28th 2008, 04:46 PM
Mathnasium
The problem statement says "0 to 2 answers," which includes the case of a single root with duplicity 2.

Remember that the "answers," which seems a poor choice of words, to a quadratic equation are also known as solutions or roots or x-intercepts.
• Mar 28th 2008, 05:10 PM
Apostolos
The equation x^2-1=0 has not only one solution...has two:-+1.the type of the quadratic that has only one solution it looks like (x-1)^2=0 or (x+1)^2=0and each solution is "double" since in this case the each graph touches the xx'axis but does not pass through to the other side.

To study all the cases seperately you should begin from the studing of the general form of the ax^2+bx+c=0 and by taking the D=b^2-4ac

you get *D=0 OR**D<0 OR***D>0 which means *no solution 0
**1 one solution double ***2 two diferent solutions.
• Mar 28th 2008, 06:01 PM
topsquark
Quote:

Originally Posted by Apostolos
The equation x^2-1=0 has not only one solution...has two:-+1.

(Ahem!) Thanks for the catch. (sheepishly wanders over to the corner muttering "My Precious!")

-Dan