Question

if -1 and 2 are two zeros of the polynomial 2 x cube minus x square - 5 x minus 2 find its third zero​

Answer 1

Answer:

Step-by-step explanation:

Attached

Answer 2

The third zero is $-\frac{1}{2}$.

Step-by-step explanation:

Given : If -1 and 2 are two zeros of the polynomial $2x^3-x^2-5x-2$

To find : Its third zero​ ?

Solution :

As -1 and 2 are two zeros of the polynomial then $(x+1)$ and $(x-2)$  product is the factor of polynomial.

i.e. $(x+1)(x-2)=x^2-2x+x-2$

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

Now, If we divide $2x^3-x^2-5x-2$ by $x^2-x-2$ we get the third factor.

As $Dividend=Divisor\times quotient +remainder$

2x^3-x^2-5x-2=(x^2-x-2)(2x+1)+0

The quotient we get is $2x+1$

Equate it to zero to get third zero.

$x=-\frac{1}{2}$

Therefore, the third zero is $-\frac{1}{2}$.

#Learn more

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