Question

How many x-intercepts appear on the graph of this polynomial function? f (x) = x Superscript 4 Baseline minus 5 x squared 1 x-intercept 2 x-intercepts 3 x-intercepts 4 x-intercepts

Answer 1

Answer:

3 x-intercepts

Step-by-step explanation:

f(x) = x⁴ - 5x²

Answer 2

Answer:

Step-by-step explanation:

Given that,

F(x) = x⁴-5x²

The x-intercept of this function occurs at f(x) = 0

Therefore,

x⁴-5x² = 0

x²(x²-5) = 0

x² = 0 OR x²-5 = 0

x = 0 twice or x² = 5

x = 0 twice or x = ±√5

So the solution to this equation is

x = 0 twice, x = √5 of x = -√5

Then, the intercept (x, y) are

(0,0) so this will only occur once

(-√5, 0)

(√5,0)

So the function has 3 x intercept which are 0,√5 and -√5