hi everyone.I'm just wondering ,if you have the roots of a quadratic equation is it possible to determine it's coefficients,i suspect i can determine b and c while a will have a range of possible values.What do you think?

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- Feb 17th 2009, 07:30 AMdynamointeresting quadratic equation problem
hi everyone.I'm just wondering ,if you have the roots of a quadratic equation is it possible to determine it's coefficients,i suspect i can determine b and c while a will have a range of possible values.What do you think?

- Feb 17th 2009, 07:46 AMADARSH
If you have the equation

x^2 + 2x - 3 = 0 You can factor the quadratic to get

(x - 1)(x + 3) = 0 and hence the roots

x = 1 and x = -3

Conversely, if you have the roots x = 1 and x = -3

you can recover the quadratic equation by forming (x - 1)(x + 3) = 0.

The same is true if the roots are complex,

for example suppose that the roots are

5 + 3i and 5 - 3i then the quadratic equation is

(x - 5 - 3i)(x - 5 + 3i) = 0

which simplifies to

x^2 - 10x + 34 = 0

Cheers,

Adarsh - Feb 17th 2009, 08:06 AMdynamothanks for replying
thanks for replying.Using the method your using suggests a is one always.I'm trying to find a way of calculating at least one of the values of a that is not one.a is the first coefficient

- Feb 17th 2009, 08:19 AMADARSH
So lets take it together

**1)**GIVEN: Roots are given

**2)**ALREADY FOUND : you found single b and c

**3)**NEXT FINDING: You found a range of "a" for a constant value of roots and other coefficients

If you agree to all the above steps than I dont agree with you

Now give a second thought and

tell me incase still you dont agree with it (Itwasntme) - Feb 17th 2009, 09:28 AMCaptainBlack
- Feb 20th 2009, 03:23 PMdynamothanks for replying
thanks for replying