Answered

Which of the following represents the zeros of f(x) = x3 − 2x2 − 6x + 12?


−2, −square root of 6, −square root of 6

2, −square root of 6, −square root of 6

2, square root of 6, −square root of 6

−2, square root of 6, square root of 6

Verified Answer :

Benjamin16

\(f(x)=x^{3}-2x^{2}-6x+12 \\ \\ x^{3}-2x^{2}-6x+12=0 \\ \\ x^{2}(x-2)-6(x-2)=0 \\ \\ (x^{2}-6)(x-2)=0 \\ \\ (x- \sqrt{6})(x+ \sqrt{6})(x-2)=0 \\ \\ x- \sqrt{6}=0 \ \vee \ x+ \sqrt{6}=0 \ \vee \ x-2=0 \\ \\ x= \sqrt{6} \ \vee \ x=- \sqrt{6} \ \vee \ x=2 \\ \\ x\in \lbrace - \sqrt{6}, 2, \sqrt{6} \rbrace\)

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This is the right answer

x=2,√6,−√6

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