Question

if 4 is a zero of a cubic polynomial
${x}^{3 } - 3 {x}^ {2} - 10x + 24$
find its other zeros​

Answer 1

Answer:

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Answer 2

AnsweR :

$\bf{\Large{\underline{\sf{Given\::}}}}$

If 4 is a zero of a cubic polynomial x³ - 3x² - 10x + 24.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The other zeroes.

$\bf{\Large{\underline{\rm{\purple{Explanation\::}}}}}$

We have,

$\leadsto\sf{x\:=\:4}\\\\Or\\\\\leadsto\sf{\red{x-4=0}}$

So, divided by x-4 to cubic polynomial, we get;

$\begin{array}{r|lllll}& x^2 & +x & -6 \\\cline{2-6} x - 4 & x^3 & -3x^2 & -10x & +24 \\ & x^3 & -4x^2 \\ & - & + \\ \cline{2-6} & & x^2 & -10x & +24 \\ & & x^2 & - 4x \\ & & -& +\\ \cline{2-6} &&& -6x & +24 \\ &&& -6x & +24 \\ &&& + & - \\ \cline{2-6} &&&&& 00\end{array}$

Now,

$|\implies\tt{x^{2} +x-6=0}\\\\\\|\implies\tt{x^{2} +3x-2x-6=0}\\\\\\|\implies\tt{x(x+3)-2(x+3)=0}\\\\\\|\implies\tt{(x+3)(x-2)=0}\\\\\\|\implies\tt{x+3=0\:\:\:\:\:\:Or\:\:\:\:\:\:x-2=0}\\\\\\|\implies\tt{\orange{x=-3\:\:\:\:\:\:Or\:\:\:\:\:\:x=2}}$

Thus,

$\bigstar$The other two zeroes are x = -3 & 2.