Can someone help me find the zeros to this equation? I have tried all possible zeros and none of them work!
Equation is : d^3+5d^2+35d+175
$\displaystyle P(d) = d^3 + 5d^2 + 35d + 175 = 0$
Use factorisation by grouping 2 and 2.
$\displaystyle 0 = d^3 + 35d + 5d^2 + 175$
$\displaystyle 0 = d(d^2 + 35) + 5(d^2 + 35)$
$\displaystyle 0 = (d^2 + 35)(d + 5)$.
Now we can use the null factor law to find the zeros.
$\displaystyle d + 5 = 0$ or $\displaystyle d^2 + 35 = 0$
The only REAL zero is $\displaystyle d = -5$, and there are 2 complex zeros, namely $\displaystyle d = \pm \sqrt{35}$.