Obtain all the zeroes of the polynomial x2+7x+10 and verify the relationship zeroes and coefficient. find all the zeroes ofthe polynomial x4+2x3-8x2-18x-9 if two of its zeroes are 3 and -3.

The first question has been answered in your previous query. So, in this query, we are answering your second query. 

 

f(x) = x4+2x3-8x2-18x-9

If its 2 roots are 3 and -3, hence f(x) is divisible by (x-3)(x+3) = x2 -9

 

Using long division to compute the quotient  = x2+2x+1

Hence f(x) = (x2-9)(x2+2x+1)

f(x) = (x-3)(x+3) (x+1)^2

 

Hence, the zeros of f(x) are 3, -3 and -1.