How many x-intercepts appear on the graph of this polynomial function? f(x)= x4-5x2

Question

asked Apr 25, 2021 122k views

2 Answers

Matthew Smart · Answer 1 · 2021-05-01T04:37:02+0000

The x-intercepts appear on this polynomial are 3 x intercepts.

Explanation:

To find the x intercepts of the polynomial
f(x)=x^(4) -5x^(2) is by equating
f(x)=0

Thus, the equation becomes

$\begin{array}{r}{x^(4)-5 x^(2)=0} \\{x^(2)\left(x^(2)-5\right)=0}\end{array}$

Equating, we get,

$x^(2)=0,\left(x^(2)-5\right)=0$

x=0 ,
$\begin{aligned}x^(2)-5 &=0 \\x^(2) &=5 \\x &=\pm √(5)\end{aligned}$

Thus, the x-intercepts are
x=0, x=√(5) , x=-√(5)

Hence, the x-intercepts appear on this polynomial are 3 x intercepts.