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?
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?
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
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