Question

sum of the zeros of the polynomials x^2-2x+1 is equal to the sum of the zeros of the polynomial x^3-2x^2+x , then find the product of all three zeros of the second polynomial . Pls help me find the method .the answer is 0

Answer 1

`x^2-2x+1=0\\\\x^2-x-x+1=0\\\\x(x-1)-1(x-1)=0\\\\(x-1)(x-1)=0\iff x-1=0\ \ \ |+1\\\\x=1\leftarrow\text{ the double zero}\\\\\text{The sum of the zeros:}\ 1+1=2`



`x^3-2x^2+x=0\\\\x(x^2-2x+1)=0\\\\x(x-1)^2=0\iff x=0\ \vee\ x=1\leftarrow\text{the double zero}\\\\\text{The sum of the zeros:}\ 0+1+1=2`


`\text{CORRECT!}`


`\text{The product of all three zeros of the second polynominal:}\\\\0\cdot1\cdot1=0`