Question #bced5

1 Answer
Nov 21, 2017

See a solution process below:

Explanation:

We can rewrite this function using this rule for quadratics:

#color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))#

#f(x) = -3x^4(color(red)(x)^2 - color(blue)(9))#

#f(x) = -3x^4(color(red)(x)^2 - color(blue)(3)^2)#

#f(x) = -3x^4(color(red)(x) + color(blue)(3))(color(red)(x) - color(blue)(3))#

Now, we can solve each term on the left side of the function for #0# to find each zero of the function:

Solution 1:

#-3x^4 = 0#

#(-3x^4)/color(red)(-3) = 0/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))x^4)/cancel(color(red)(-3)) = 0#

#x^4 = 0#

#root(4)(x^4) = root(4)(0)#

#x = 0#

Solution 2:

#x + 3 = 0#

#x + 3 - color(red)(3) = 0 - color(red)(3)#

#x + 0 = -3#

#x = -3#

#x = 0#

Solution 3:

#x - 3 = 0#

#x - 3 + color(red)(3) = 0 + color(red)(3)#

#x - 0 = 3#

#x = 3#

The Solutions Are: #x = {-3, 0, 3}#

The graph of the function touch the #x#-axis at #0#:

graph{y + 3x^6 - 27x^4 = 0 [-10, 10, -50, 400]}