Question

One zero of f(x)=x^3-2x^2-5+6 is 1 what are the other zeros of the function

Answer 1

the other zeros of this function are {-2, 3}

Explanation:

Use synthetic division to find the roots. The coefficients of this cubic function are 1, -2, -5, 6, and we begin by using 1 as our first divisor:

1 / 1 -2 -5 6

+1 -1 -6

--------------------------

1 -1 -6 0

Because the remainder is zero (0), we can conclude that 1 is indeed a root of the given polynomial. The quotient is 1x^2 - 1x - 6, whose roots can be found either through synthetic division or factoring. In this case the factors are (x - 3) and (x + 2), so the other zeros of this function are {-2, 3}.