Question

Find a cubic polynomial whose zeroes are 1/2,-1,2​

Answer 1

$\textbf{Given:}$

$\textsf{Zeroes are}\;\mathsf{\dfrac{1}{2},-1,2}$

$\textbf{To find:}$

$\textsf{The polynomial having the given zeroes}$

$\textbf{Solution:}$

$\textsf{The required polynomial can be written as}$

$\mathsf{(x-\frac{1}{2})(x+1)(x-2)}$

$\mathsf{=(x-\frac{1}{2})(x^2-x-2)}$

$\mathsf{=x^3-x^2-2x-\frac{1}{2}x^2+\frac{1}{2}x+1}$

$\mathsf{=x^3-\frac{5}{2}x^2-\frac{3}{2}x+1}$

$\implies\boxed{\mathsf{x^3-\frac{5}{2}x^2-\frac{3}{2}x+1}}$

$\textbf{Find more:}$

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

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