Question

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

     

$p(x)=3x^3+10x^2-9x-4$

$Dividing \ \ p(x)\ \ by \ \ (x-1), \\ \\ \\ [Because 1 is a root of \ \ p(x)]$

$3x^3+10x^2-9x-4 \\ \\ \Rightarrow\ 3x^3-3x^2+13x^2-13x+4x-4 \\ \\ \Rightarrow\ 3x^2(x-1)+13x(x-1)+4(x-1) \\ \\ \Rightarrow\ (x-1)(3x^2+13x+4) \\ \\ \Rightarrow\ (x-1)(3x^2+x+12x+4) \\ \\ \Rightarrow\ (x-1)(x(3x+1)+4(3x+1)) \\ \\ \Rightarrow\ (x-1)(x+4)(3x+1) \\ \\ \\ \therefore\ x=\bold{-4}\ \ \ ; \ \ \ x=-\bold{\frac{1}{3}}$

$\therefore\ The other zeroes are \ \bold{-4}\ \ \&\ \ \bold{-\frac{1}{3}}. \\ \\ \\ Plz ask me if you have any doubt on my answer. \\ \\ \\ Thank you. :-))$

$\mathfrak{\#adithyasajeevan}$