Help! How to factorise x^3 - 9x^2 + 24x - 30?
It seems according to the key, 2 roots are imaginary and 1 root is real.
I need to know only the real one. Can someone please help!!!!!
It doesn't factorise.
A sketch graph shows that there is a single real root to the right of x = 4,
and a table of values narrows it to between x = 5 and x = 6.
You can get a better approximation if you wish, but you are then into your favourite numerical method.
Hello, mathhawk!
Help! .How to factorise: $\displaystyle f(x) \:=\:x^3 - 9x^2 + 24x - 30\,?$
According to the key, 2 roots are imaginary and 1 root is real.
It is not factorable.
The only possible rational roots are: .$\displaystyle \pm1,\:\pm2,\:\pm3,\:\pm5,\:\pm6,\:\pm10,\:\pm15, \:\pm30$
. . None of them are zeros of the polynomial.
We find that: .$\displaystyle \begin{Bmatrix}f(5) &=& \text{-}10 \\ f(6) &=& +6 \end{Bmatrix}$
Hence, there is a root (irrational) on the interval $\displaystyle (5,\,6).$
Another possibility: a typo in the problem.
. . Could the constant term be -20 or -36?