Use the zero or root feature of a graphing utility to approximate the real zeros of the function $f ( x ) = x ^ { 6 } - 4 x ^ { 4 } + x ^ { 2 } + 6$ accurate to the nearest thousandth.
A) $\pm 1$ , 1.732, 1.414
B)-1.732, -1.414
C) $\pm$ 1.732, $\pm$ 1.414
D)1.732, 1.414
E) $\pm 1$ , - 1.732, 1.414

Question

Quizplus · Accepted Answer

The real zeros of the function can be found using a graphing utility. By plotting the function $f(x) = x^6 - 4x^4 + x^2 + 6$ and using the zero or root feature, we can identify the points where the graph crosses the x-axis. The symmetry of the function and the nature of its terms suggest that if $x$ is a root, then $-x$ is also a root, due to all powers of $x$ being even. The correct roots, accurate to the nearest thousandth, include both positive and negative versions of approximately 1.732 and 1.414, which corresponds to the roots of the given polynomial equation.

Use the Zero or Root Feature of a Graphing Utility f(x)=x6−4x4+x2+6f ( x ) = x ^ { 6 } - 4 x ^ { 4 } + x ^ { 2 } + 6f(x)=x6−4x4+x2+6

Use the Zero or Root Feature of a Graphing Utility $f ( x ) = x ^ { 6 } - 4 x ^ { 4 } + x ^ { 2 } + 6$