# Probability with relation to Quadratic Equation

• Jul 11th 2011, 01:11 PM
somster100
{SOLVED} Probability with relation to Quadratic Equation
First of all, I would like to thank each and everyone of you who is viewing this post. I know that you personally have helped many students with their questions and I know that by posting here, Im sure to get the right response !

Heres the Question :

3) Suppose we begin with the quadratic equation

We know the roots of the equation are given by the quadratic formula,

Now let a, b, and c be all positive single digit integers (that is, from 1 to 9). For example, one such quadratic equation can be (a=3, b=4, c=1)

Of all the possible quadratic equations of this type, if one equation is randomly picked, what is the probability that the roots of the equation will be rational?

hopefully someone can help me with this question ! (Happy)
• Jul 11th 2011, 03:34 PM
mr fantastic
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by somster100
First of all, I would like to thank each and everyone of you who is viewing this post. I know that you personally have helped many students with their questions and I know that by posting here, Im sure to get the right response !

Heres the Question :

3) Suppose we begin with the quadratic equation

We know the roots of the equation are given by the quadratic formula,

Now let a, b, and c be all positive single digit integers (that is, from 1 to 9). For example, one such quadratic equation can be (a=3, b=4, c=1)

Of all the possible quadratic equations of this type, if one equation is randomly picked, what is the probability that the roots of the equation will be rational?

hopefully someone can help me with this question ! (Happy)

• Jul 11th 2011, 06:24 PM
somster100
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by mr fantastic

So I narrowed down the question in being

- What is the probability of b^2 - 4ac being a perfect square using intergers from 1-9

Can anybody help me solve this please?
• Jul 11th 2011, 08:38 PM
mr fantastic
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by somster100
So I narrowed down the question in being

- What is the probability of b^2 - 4ac being a perfect square using intergers from 1-9

Can anybody help me solve this please?

Can't you substitute b = 1 and see what must happen for a and c. Then substitute b = 2 and see what must happen for a and c etc. .... So you count the number of triplets (b, a, c) that satisfy the condition. And what is the total number of unrestricted triplets ....? Divide by those two numbers.
• Jul 11th 2011, 08:47 PM
somster100
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by mr fantastic
Can't you substitute b = 1 and see what must happen for a and c. Then substitute b = 2 and see what must happen for a and c etc. .... So you count the number of triplets (b, a, c) that satisfy the condition. And what is the total number of unrestricted triplets ....? Divide by those two numbers.

That works ! but why divide by those two numbers?
• Jul 11th 2011, 08:50 PM
mr fantastic
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by somster100
That works ! but why divide by those two numbers?

Doesn't the question ask for a probability ...? And you will have learned that Pr(favourable outcome) = (Number of favourable outcomes)/(Total number outcomes) ....?
• Jul 11th 2011, 08:52 PM
somster100
This is taking wayyy to long to find each and every possibily -- # of faborable outcomes
is there any other way of finding this?

there must be another way for finding all the outcomes :(
• Jul 11th 2011, 09:14 PM
mr fantastic
Re: Probability with relation to Quadratic Equation
Quote:

Originally Posted by somster100
there must be another way for finding all the outcomes :(

The total number of triplets (b, a, c) where a, b and c are defined in post #1 is obviously 9^3.

As for the favourable triplets, it surely doesn't take all that long to list them, especially since the discriminant can't be negative and the perfect square can't be larger than 81 ....