Find all x-intercepts of the function.
-$$f ( x ) = x ^ { 4 } - 13 x ^ { 2 } + 36$$
A) $$( \pm 2,0 ) , ( \pm 3,0 )$$
B)(2, 0), (3, 0)
C)(4, 0), (9, 0)
D) $$( \pm 2 \mathrm { i } , 0 ) , ( \pm 3 \mathrm { i } , 0 )$$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the function $f(x) = x^4 - 13x^2 + 36$, we set $f(x) = 0$ and solve for $x$. This gives us the equation $x^4 - 13x^2 + 36 = 0$. This can be seen as a quadratic equation in terms of $x^2$, where $x^2 = y$, leading to $y^2 - 13y + 36 = 0$. Factoring or using the quadratic formula gives $y = 4$ or $y = 9$, which means $x^2 = 4$ or $x^2 = 9$. Therefore, $x = \pm 2$ or $x = \pm 3$, corresponding to the x-intercepts $(\pm 2,0)$ and $(\pm 3,0)$.

Find All X-Intercepts of the Function f(x)=x4−13x2+36f ( x ) = x ^ { 4 } - 13 x ^ { 2 } + 36f(x)=x4−13x2+36

Find All X-Intercepts of the Function $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } + 36$