K
khorne
Guest
Hey
I have a question:
x^3 +mx^2 +15x - 7 = 0 and has two equal roots, find m:
Firstly, I constructed the roots equations:
2a + b = -m
a^2 + 2ab = 15
a^2b = 7
And then, (with help from Mr Squidge) differentiated, as P(x)=P'(x) = 0 (on a double root)...and got the additional equation of 3x^2 + 2mx + 15 =0
However, no amount of fiddling with these equations gives an answer for any root, let alone m...So can anyone suggest anything?
I know it can be done by (x-a)(x-a)(x-b) and from inspection, b = 7, a = 1, but this was under the polynomial roots heading, so I'm pretty sure I have to use roots.
Thanks
I have a question:
x^3 +mx^2 +15x - 7 = 0 and has two equal roots, find m:
Firstly, I constructed the roots equations:
2a + b = -m
a^2 + 2ab = 15
a^2b = 7
And then, (with help from Mr Squidge) differentiated, as P(x)=P'(x) = 0 (on a double root)...and got the additional equation of 3x^2 + 2mx + 15 =0
However, no amount of fiddling with these equations gives an answer for any root, let alone m...So can anyone suggest anything?
I know it can be done by (x-a)(x-a)(x-b) and from inspection, b = 7, a = 1, but this was under the polynomial roots heading, so I'm pretty sure I have to use roots.
Thanks
