Question

Find all zeros of the polynomial 3x³ + 10x² − 9x − 4 if one of its zero is 1. 

Answer 1

Given: 3x³ + 10x² - 9x - 5 

Since 1 is a zero of the given polynomial. So, (x - 1) will be a factor of the given polynomial. 

So, 3x³ + 10x² - 9x - 4 = (x - 1)(3x² + 13x + 4) 

By splitting the middle term in (3x² + 13x + 4) we factorised (3x² + 13x + 4) as (3x + 1)(x + 4).

So, the zeroes are given by x = -4, `(-1)/3` 

Thus, all the zeroes are x = -4, `(-1)/3,1`