## anonymous one year ago Can anyone plz help me? I'm trying to solve this polynomial equation: x^3-14x^2+47x-18=0

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1. triciaal

ok the highest power is 3 so maximum of 3 roots the constant is -18 so a factor of 18 will be one of the roots (factors of 18 are 1, 2, 3, 6, 9 and the negatives ) don't remember the easy way to do this but in either case when you have a root then (x-root) is a factor in addition when you have a root then f(root) = zero eg if 2 is a root then f(2) = 0 divide by a factor then factorize the quadratic to find the others

2. triciaal

|dw:1439354933156:dw|

3. triciaal

|dw:1439355454429:dw||dw:1439355715418:dw|

4. triciaal

|dw:1439356453827:dw|

5. triciaal

|dw:1439356892355:dw|

6. triciaal

sorry this is so messy and I am all over but hope something helped.

7. DecentNabeel

$x^3-14x^2+47x-18=0\quad :\quad x=\frac{5+\sqrt{17}}{2},\:x=\frac{5-\sqrt{17}}{2},\:x=9$

8. DecentNabeel

$\mathrm{Factor}\:x^3-14x^2+47x-18:\quad \left(x-9\right)\left(x^2-5x+2\right)$ $\left(x-9\right)\left(x^2-5x+2\right)=0$ $\mathrm{Using\:the\:Zero\:Factor\:Principle:}$ $\mathrm{Solve\:}\:x-9=0:\quad x=9$ $\mathrm{Solve\:}\:x^2-5x+2=0:\quad x=\frac{5+\sqrt{17}}{2},\:x=\frac{5-\sqrt{17}}{2}$