Question

if two zeros of x3+x2-5x-5 are root 5 and -root5 then its third zero is'

Answer 1

Answer:

Step-by-step explanation:

The answer is given below......  

Answer 2

Answer:

Required third zero or root is (-1)

Step-by-step explanation:

Given polynomial is ${x}^{3} + {x}^{2} - 5x - 5$

Let,$f(x) = {x}^{3} + {x}^{2} - 5x - 5$

f(x) is a three degree polynomial.

So,f(x)=0 has three zero.

Given,$\sqrt{5}$and $( - \sqrt{5} )$are two zeros of $f(x) = 0$

Let another root is y.

So we can write,${x}^{3} + {x}^{2} - 5x - 5 = (x - \sqrt{5} )(x + \sqrt{5} )(x - y) \\ {x}^{3} + {x}^{2} - 5x - 5 = ( {x}^{2} - { \sqrt{5} }^{2} )(x - y) = ( {x}^{2} - 5)(x - y) \\ {x}^{3} + {x}^{2} - 5x - 5 = {x}^{3} - y {x}^{2} - 5x + 5y$

We are comparing both side and get,

$- y = + 1$

So,

$y = - 1$

and 5y=-5

So,y=-1

Therefore,required third zero or root is (-1)