Find all x-intercepts of the function.
-$$f ( x ) = x ^ { 4 } - 21 x ^ { 2 } + 80$$
A) $$( 4,0 ) , ( \sqrt { 5 } , 0 )$$
B) $$( \pm 4,0 ) , ( \pm \sqrt { 5 } , 0 )$$
C) $$( \pm 4,0 ) , ( \pm \mathrm { i } \sqrt { 5 } , 0 )$$
D)(16, 0), (5, 0)

Question

Quizplus · Accepted Answer

To find the x-intercepts of the function $f(x) = x^4 - 21x^2 + 80$, we set $f(x) = 0$ and solve for $x$. This gives us the equation $x^4 - 21x^2 + 80 = 0$. We can solve this equation by treating it as a quadratic equation in terms of $x^2$, i.e., let $y = x^2$, then the equation becomes $y^2 - 21y + 80 = 0$. Factoring or using the quadratic formula gives us $y = 16$ and $y = 5$, which means $x^2 = 16$ and $x^2 = 5$. Solving for $x$ gives $x = \pm4$ and $x = \pm\sqrt{5}$, respectively. Therefore, the x-intercepts are $(\pm4, 0)$ and $(\pm\sqrt{5}, 0)$.

Find All X-Intercepts of the Function f(x)=x4−21x2+80f ( x ) = x ^ { 4 } - 21 x ^ { 2 } + 80f(x)=x4−21x2+80

Find All X-Intercepts of the Function $f ( x ) = x ^ { 4 } - 21 x ^ { 2 } + 80$