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?

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) (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:

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

Combine the x-terms and put in common denominator

Step 3. ANSWER:

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) (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:

Multiplying this out we get:

Adding like terms we get:

So our quadratic equation is:

If we don't want fractions, multiply both sides by 3:

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