Question

Write the polynomial in x whose zeroes are 1,2 and -1

Answer 1

Answer:

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

Step-by-step explanation:

If a polynomial in x has zeros 1,2 and -1, then it has the following factors

(x-1), (x-2) and (x+1)

Therefore;

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

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The polynomial is }}}x^2+2x^2-x-2.$

Step-by-step explanation:

We know that if a polynomial in x has zeroes a, b and c, then the polynomial can be written as follows :

$p(x)=(x-a)(x-b)(x-c).$

Therefore, the polynomial in x with zeroes 1, 2 and -1 can be written as

$p(x)\\\\=(x-1)(x-2)(x-(-1))\\\\=(x-1)(x-2)(x+1)\\\\=(x^2-1)(x+2)\\\\=x^3+2x^2-x-2.$

Thus, the required polynomial is $x^3+2x^2-x-2.$

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Question : Write the polynomial of 'x' whose zeroes are 1, -1, 2.

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