SOLUTION: 3. Use the two roots given by the quadratic equation a. find a formula for the sum of the roots b. find a formula for the product of the roots c. without solving tell the sum an

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 3. Use the two roots given by the quadratic equation a. find a formula for the sum of the roots b. find a formula for the product of the roots c. without solving tell the sum an      Log On


   

Question 187810: 3. Use the two roots given by the quadratic equation
a. find a formula for the sum of the roots
b. find a formula for the product of the roots
c. without solving tell the sum and product of the solutions of 2x^2+5x-3=0
I don't even understand the question at all....I feel like it doesn't make sense
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the quadratic formula is

x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29


which really breaks down to


x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 or x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29


where x%5B1%5D and x%5B2%5D are the two roots


a)

find a formula for the sum of the roots


x%5B1%5D%2Bx%5B2%5D Add the roots x%5B1%5D and x%5B2%5D


%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29%2B%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Plug in the formulas from above.


%28-b+%2B+sqrt%28+b%5E2-4ac+%29+-+b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Combine the fractions


%28-2b%29%2F%282a%29 Combine like terms.


-b%2Fa Reduce


So the sum of the roots x%5B1%5D and x%5B2%5D is -b%2Fa


In other words, x%5B1%5D%2Bx%5B2%5D=-b%2Fa



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b)

find a formula for the product of the roots


x%5B1%5D%2Ax%5B2%5D Multiply the two roots.


Plug in the formulas above


Combine the fractions.


%28%28-b%29%5E2+%2B+%28sqrt%28+b%5E2-4ac+%29%29%5E2%29%2F%28%282a%29%282a%29%29 FOIL by using the difference of squares formula


%28b%5E2-%28b%5E2-4ac%29%29%2F%284a%5E2%29 Square each term.


%28b%5E2-b%5E2%2B4ac%29%2F%284a%5E2%29 Distribute


%284ac%29%2F%284a%5E2%29 Combine like terms.


c%2Fa Reduce


So the formula for the product of the roots x%5B1%5D and x%5B2%5D is c%2Fa


In other words, x%5B1%5D%2Ax%5B2%5D=c%2Fa


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c)

without solving tell the sum and product of the solutions of 2x^2+5x-3=0


From 2x%5E2%2B5x-3=0, we see that a=2, b=5, and c=-3


Sum of the roots: x%5B1%5D%2Bx%5B2%5D=-b%2Fa=-5%2F2


Product of the roots: x%5B1%5D%2Ax%5B2%5D=-3%2F2