find all the zeroes of the polynomial 3x cube + 10x square - 9x - 4 if one of its zeroes is 1
Answers
Given : polynomial 3x³ + 10x² - 9x - 4
one zero is 1
To Find : All the zeroes
Solution:
3x³ + 10x² - 9x - 4
one zero is 1 => x- 1 is one of the factor
3x² + 13x + 4
x - 1 _| 3x³ + 10x² - 9x - 4 |_
3x³ - 3x²
___________
13x² - 9x - 4
13x² - 13x
___________
4x - 4
4x - 4
___________
0
3x² + 13x + 4
= 3x² + 12x +x + 4
= 3x(x + 4) + 1(x + 4)
= (3x + 1)(x + 4)
3x + 1 = 0 => x = -1/3
x + 4 = 0 => x = - 4
Other zeroes are - 1/3 , - 4
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