Question

Form a cubic polynomial whose zeroes are 2 , 1 , 1.

Answer 1

$\textbf{Given:}$

$\text{zeros are 2,1,1}$

$\textbf{To find:}$

$\text{A cubic polynomial having zeros 2,1,1}$

$\textbf{Solution:}$

$\text{We know that}$

$\text{A cubic polynomial whose zeros a,b and c is}$

$\boxed{\bf\,x^3-(a+b+c)x^2+(ab+bc+ca)x-abc}$

$\text{The required cubic polynomial is}$

$x^3-(a+b+c)x^2+(ab+bc+ca)x-abc$

$=x^3-(2+1+1)x^2+((2)(1)+(1)(1)+(1)(2))x-(2)(1)(1)$

$=x^3-(2+1+1)x^2+(2+1+2)x-2$

$=x^3-4x^2+5x-2$

$\textbf{Answer:}$

$\boxed{\bf\,x^3-4x^2+5x-2}$

Find more:

Obtain all the zeros of the polynomial 3x^3+10x^2-9x-4 if one of its zero is 1

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