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