# Finding the Roots

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• Sure, you just solve the polynomial equation by finding all roots
• Can you help me solve 2x^3-12x^2-3x+204=0
• Ok, how do we start this?
• 2(x^3-6x^2-17x+102)=0
• First you find the greatest common factor and that is 2.
• 2[(x^3-6x^2)(17x+102)]=0 [x^2(x-6)-17(x-6)]=0
• Is the part where 'Poly' comes to play? Do we make new equations?
• Yes, I guess. You group the fist two then the next. Then you factor out.
• 2(x-6)(x^2-17)=0
• Are we almost doneeeee?
• No..we have to put it together then actually find the zeros/roots.
• Now we set each parenthesis to zero right?
• (x-6)=0 x=6 (x^2-17)=0. x=the square root of 17 x= negative the square root of 17
• Yes...I thought you didn't know how to do this.
• Can you explain why that split in two please?
• Sure, when you are square rooting this, you have to put plus of minus.
• Since you put plus or minus there are now two equations.
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