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  • Obtain all other zerses of the polynomial p(x)=x4+6x3+x2-24x-20 if two of its zeroes are +2 and -5​

Obtain all other zerses of the polynomial p(x)=x4+6x3+x2-24x-20 if two of its zeroes are +2 and -5​

Answers (1)

Given, Two of zeroes are 2 and (-5)

According to FACTOR THEOREM, (x-2) and (x+5) will be factors are p(x)

Then

\\ $(x-2)(x+5)$\\ $=x^{2}+5 x-2 x-10$ \\ $=x^{2}+3 x-10$ \\ $x^{2}+3 x-10$\ \text{is also a factor of p(x)}

\\ \text{Now, By Dividing} \ p(x)\ by\ x^{2}+3 x-10\\ We\ get: \\ $Q(x)=x^{2}+3 x+2$\ and \ remainder=0

\begin{array}{l} p(x)=\left(x^{2}+3 x-10\right)\left(x^{2}+3 x+2\right) \\ =(x-2)(x+5)\left(x^{2}+x+2 x+2\right) \\ =(x-2)(x+5)(x+1)(x+2) \end{array}

So zeros of p(x) are 2,-5,-1,-2

Posted by

shubham.krishnan

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