SOLUTION: Could someone help me with these: What is the sum of the roots of the equation ax^2+bx+c=0 ? What is the product of their roots? How would I solve this equation x^3+2x^2+x+2=0,

Question 199257: Could someone help me with these:
What is the sum of the roots of the equation ax^2+bx+c=0 ?
What is the product of their roots?
How would I solve this equation x^3+2x^2+x+2=0, if -2 is a root?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The roots are:
(-b/2a) + sqrt(b^2-4ac)/2a and (-b/2a) - sqrt(b^2-4ac)/(2a)
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What is the sum of the roots of the equation ax^2+bx+c=0 ?
sum = 2(-b/2a) = -b/a
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What is the product of their roots?
product is [b/2a]^2 - [sqrt(b^2-4ac)/2a]^2
= [b^2/4a^2] - [(b^2-4ac)/(4a^2)
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How would I solve this equation x^3+2x^2+x+2=0, if -2 is a root?
Use synthetic division:
-2)....1....2....1....2
.........1...0....1....|..0
Quotient: x^2 +1
Remainder:0
------------------------
Solving x^2+1 = 0
(x+i)(x-i) = 0
==========================
Solutions: x = -2, x = i, x = -i
------------------------------------------------------------------
Cheers,
Stan H.
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