Determine the x-intercepts of the polynomial function y=-6(x+7)^4 + 5. Round to two decimal places, if necessary.

Answer 1

The x axis intercepts are where y = 0
0 = -6(x+7)^4 + 5
(x+7)^4 = 5/6 = 0.8333 ....
(x+7)^2 = +/- 0.91287
if (x+7)^2 = + 0.91287
then
x+7 = +/- 0.977468
or
x = -7.977 or -6.0225
That is two of the four
now if
(x+7)^2 = -0.91287
then
(x+7) = +i sqrt 0.91287
and
(x+7) = -i sqrt 0.91287
so
x = -7 +/- 0.955 i