the answer
the complement of the question is perhaps the function
f(x)= x4 - 5x2
to find the value of x-intercepts, just egalize f(x)= x4 - 5x2 to 0, and solve the equation.
that is x4 - 5x2 = 0 equivalent to x²(x²-5) = 0, this implies x²-5 = 0 and x²=0,
it implies x=0 and x²= 5, which means x = +/- sqrt(5)
so the x intercepts are x=0, x = - sqrt(5) and x = +sqrt(5)
finally the answer is 3 x intercepts
According to the Fundamental Theorem of Algebra, we will find which polynomial function has exactly 8 roots
the number of roots is equal to the highest degree of the polynomial functions
among the 4 functions,
b.f(x)to the 5th power+3xto the 4th power+12xcubed+7xsquared -2x+15
is unknown (something is lack at the first term)
the 3 others doesn't match to the question, so it depends on the " choice b"
by contrast,
According to the Fundamental Theorem of Algebra, the polynomial function that has exactly 6 roots is
d.f(x)7xto the 6th power+3xcubed+12 (the degree is 6)