Use the zero or root of graphing utility to find the real zeros of the function $f ( x ) = x ^ { 4 } = 3 x ^ { 2 } - 5 x ^ { 2 } - 21 x + 22$ and find the exact values of the remaining zeros.
A)Real zeros: $2,3$ Exact zero: $- 3 \pm \sqrt { 2 } i$
B)Real zeros: $2,3$ Exact zero: $- 3 - \sqrt { 2 } i$
C)Real zeros: $1,2$ Exact zero: $3 \pm \sqrt { 2 } i$
D)Real zeros: $1,2$ Exact zero: $3 + \sqrt { 2 } i$
E)Real zeros: $1,2$ Exact zero: $- 3 \pm \sqrt { 2 } i$

Question

Quizplus · Accepted Answer

The given function seems to have a typographical error. Assuming the correct function is $f(x) = x^4 + 3x^3 - 5x^2 - 21x + 22$, solving this equation through factoring or using a graphing utility can help identify the real zeros. Polynomial division or synthetic division, along with the Rational Root Theorem, can be used to find that 1 and 2 are real zeros. The remaining quadratic can be solved using the quadratic formula, leading to complex zeros of the form $-3 \pm \sqrt{2}i$.

Use the Zero or Root of Graphing Utility to Find f(x)=x4=3x2−5x2−21x+22f ( x ) = x ^ { 4 } = 3 x ^ { 2 } - 5 x ^ { 2 } - 21 x + 22f(x)=x4=3x2−5x2−21x+22

Use the Zero or Root of Graphing Utility to Find $f ( x ) = x ^ { 4 } = 3 x ^ { 2 } - 5 x ^ { 2 } - 21 x + 22$