Question

Obtain the zeroes of the polynomial 9x^4-6x^3-35x^2+24x-4

Answer 1

$p(x) = 9{x}^{4} - 6 {x}^{3} - 35 {x}^{2} + 24x - 4$
This will have the same zeroes as:
$q(x) = {x}^{4} - \frac{6}{9} {x}^{3} - \frac{35}{9} {x}^{2} + \frac{24}{9} x - \frac{4}{9} \\ q(x) = {x}^{4} - \frac{2}{3} {x}^{3} - \frac{35}{9} {x}^{2} + \frac{8}{3} x - \frac{4}{9}$
By Rational Root Theorem, Roots are:
$\frac{1}{3} \: \: \: \: \frac{1}{3} \: \: \: \: 2 \: \: \: \: - 2$

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