Question

Functions f and g are defined for all real numbers. The function f has zeroes at -2, 3, and 7; and the function g has zeroes at -3, -1, 4, and 7. How many distinct zeroes dose the product function f * g have? Explain and show your answer.

Answer 1

SOLUTION;

there are two polynomial function

For first polynomial function;

There degree=3

And zero's is -2,3,7

To the function is.

f(x)=(x+2)(x-3)(x-7).....(1)

For 2nd polynomial function

g(x) is degree =4

And zeros are =-3,-1,4,7

Then, there polynomial function is

g(x)=(x+3)(x+1)(x-4)(x-7)

Then,

For product of f(x)and g(x) is resultant degree = 7

f*g(x) is =(x+2)(x-3)(x-7)(x+3)(x+1)(x-4)(x-7)

Then the real zero =total number of 7 is zeros

Answer =7