Question

How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2.

1 x intercept
2 x intercepts
3 x intercepts
4 x intercepts

Answer 1

x-intercepts are the points where the graph crosses the x-axis. Along the x-axis value of y-coordinate is zero. So if we equate the given equation to 0, we can find the points where y-coordinate is zero and thus we can find the x-intercepts of F(x).


`0= x^(4)- 5^(2) \\ \\ 25= x^(4) \\ \\`

Taking square root of both sides we get:


`(5) = x^(2) , \\ -5= x^(2)`

The square root of -5 will result in a complex number. So we reject this value and only consider
`5= x^(2)`

Taking the square root again, we get:

`+- √(5)=x`

Thus the F(x) has two x-intercepts at
`x= √(5)` and
`x= -√(5)`