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