SOLUTION: What would the quadratic eqation be with the roots 2/3 and 4. i got this question on a test and i didnt know how to do it can someone help please?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: What would the quadratic eqation be with the roots 2/3 and 4. i got this question on a test and i didnt know how to do it can someone help please?      Log On


   

Question 223003: What would the quadratic eqation be with the roots 2/3 and 4. i got this question on a test and i didnt know how to do it can someone help please?
Found 2 solutions by drj, jsmallt9:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
What would the quadratic eqation be with the roots 2/3 and 4. i got this question on a test and i didnt know how to do it can someone help please?

Step 1. Since you know these are roots they satisfy the following equation:

%28x-2%2F3%29%28x-4%29=0

Step 2. Use the FOIL method to multiply out the terms and to get rid of the parenthesis.


%28x-2%2F3%29%28x-4%29=x%2Ax-4%2Ax-2x%2F3%2B%28-2%2F3%29%2A%28-4%29


%28x-2%2F3%29%28x-4%29=x%5E2-4x-2x%2F3%2B8%2F3

Combine the x-terms and put in common denominator

%28x-2%2F3%29%28x-4%29=x%5E2-%284%2B2%2F3%29x%2B8%2F3

%28x-2%2F3%29%28x-4%29=x%5E2-%2812%2F3%2B2%2F3%29x%2B8%2F3

%28x-2%2F3%29%28x-4%29=x%5E2-14x%2F3%2B8%2F3

Step 3. ANSWER: %28x-2%2F3%29%28x-4%29=x%5E2-14x%2F3%2B8%2F3

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J



Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this and similar problems is to understand that if some number, let's call it "r", is a root of a polynomial, let's call it P(x), then (x-r) is a factor of P(x) (and vice versa).

So a polynomial with roots of 2/3 and 4 would be:
P%28x%29+=+%28x+-+2%2F3%29%28x-4%29
Multiplying this out we get:
P%28x%29+=+x%5E2+-4x+-+%282%2F3%29x+%2B+8%2F3
Adding like terms we get:
P%28x%29+=+x%5E2+-+%2814%2F3%29x+%2B+8%2F3
So our quadratic equation is:
x%5E2+-+%2814%2F3%29x+%2B+8%2F3+=+0
If we don't want fractions, multiply both sides by 3:
3x%5E2+-+14x+%2B+8+=+0+