Find all zeros of function and write the polynomial as a product of linear factorsX^3-x^2+9x-9

Mathematics

1 answer:

mart [117]3 years ago

8 0

Answer:

$\large\boxed{x=1\ \vee\ x=-3i\ \vee\ x=3i}$

Step-by-step explanation:

$\text{The zeros:}\\\\x^3-x^2+9x-9=0\\\\x^2(x-1)+9(x-1)=0\\\\(x-1)(x^2+9)=0\iff x-1=0\ \vee\ x^2+9=0\\\\x-1=0\qquad\text{add 1 to both sides}\\x-1+1=0+1\\\boxed{x=1}\\\\x^2+9=0\qquad\text{subtract 9 from both sides}\\x^2=-9$

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