Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$H ( x ) = x ^ { 6 } + 26 x ^ { 3 } - 27$$
A) $x = - 3 , x = 1$
B) $x = 3$
C) $x = 27$
D) $x = 3 , x = - 1$

Question

Quizplus · Accepted Answer

To find the real zeros of the function, we can factor the given polynomial. Let $y = x^3$, then the equation becomes $y^2 + 26y - 27 = 0$. Factoring this quadratic equation, we get $(y + 27)(y - 1) = 0$, so $y = -27$ or $y = 1$. Substituting back $x^3$ for $y$, we get $x^3 = -27$ and $x^3 = 1$. Solving these equations gives $x = -3$ and $x = 1$, which are the real zeros of the function and thus the x-intercepts of its graph.

Find the Real Zeros of the Function H(x)=x6+26x3−27H ( x ) = x ^ { 6 } + 26 x ^ { 3 } - 27H(x)=x6+26x3−27

Find the Real Zeros of the Function $H ( x ) = x ^ { 6 } + 26 x ^ { 3 } - 27$