Answer:
Touches at -3 and crosses at 3.5
Step-by-step explanation:
f(x)=(2x-7)^7 (x+3)^4 is given
To find x intercepts:
for x intercepts the value of f(x) =0
Hence f(x)=(2x-7)^7 (x+3)^4=0
Solving we get
2x-7 =0 or x+3 =0
x = 3.5 or x=-3
Thus we find the zeroes of the polynomial of f(x) are 3.5 and -3.
3.5 has a multiplicity of 7 and -3 a multiplicity of 4
Since 7 is odd, i.e. 3.5 has a multiplicity of odd number, hence f(x) crosses x axis at x 3.5
Since -3 has a multiplicity of an even number 4, we find that the curve touches x axis at the point -3.
