Write the polynomial in standard form and identify the zeros of the function.
-$$f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )$$
A) $f ( x ) = x ^ { 3 } - x ^ { 2 } + 7 x - 7 ;$ zeros $1 , \pm \sqrt { 7 } i$
B) $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ; \operatorname { zeros } 1 , \pm \sqrt { 7 } i$
C) $f ( x ) = x ^ { 3 } - x ^ { 2 } + 49 x - 49$; zeros $1 , \pm 7 i$
D) $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ;$ zeros $- 1 , \pm \sqrt { 7 } i$

Question

Quizplus · Accepted Answer

Multiplying the factors gives $f(x) = (x - 1)[(x - \sqrt{7}i)(x + \sqrt{7}i)] = (x - 1)(x^2 + 7)$, which simplifies to $x^3 - x^2 + 7x - 7$. The zeros are $1, \pm \sqrt{7}i$.

Write the Polynomial in Standard Form and Identify the Zeros f(x)=(x−1)(x−7i)(x+7i)f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )f(x)=(x−1)(x−7​i)(x+7​i)

Write the Polynomial in Standard Form and Identify the Zeros $f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )$