What are all the possible rational zeros for #f(x)=x^3-10x^2+16x+15# and how do you find all zeros?
1 Answer
Explanation:
#f(x) = x^3-10x^2+16x+15#
By the rational roots theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1, +-3, +-5, +-15#
We find:
#f(3) = 27-90+48+15 = 0#
So
#x^3-10x^2+16x+15 = (x-3)(x^2-7x-5)#
We can find the zeros the remaining quadratic
#x = (-b+-sqrt(b^2-4ac))/(2a)#
#color(white)(x) = (7+-sqrt((-7)^2-4(1)(-5)))/(2*1)#
#color(white)(x) = (7+-sqrt(49+20))/2#
#color(white)(x) = 7/2+-sqrt(69)/2#