Question

if 1 and minus 2 at 2 zeros of the polynomial x cube minus 4 x square - 7 x + 10 find its third zero

Answer 1

(x-1)(x+2)=0
x square plus 2x -x-2=0
x square plus x -2 ....................1


Now divide p(x) with 1

Now u will get x-5 as quotient
so third zero will be 5

Answer 2

The third zero of the given equation is x = 5.

Solution:

Given that polynomial equation is:-

$x^{3}-4 x^{2}-7 x+10=0$

And the 2 zeros (factors) of the above equation are  

x=1 and x=-2

Therefore,  

The two factors are  

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

Then the combined factor is found by multiplying the factors,

$x^{2}+x-2$ is the factor.

Then dividing the given polynomial equation $x^{3}-4 x^{2}-7 x+10=0$, By the combined factor $x^{2}+x-2$ we get x-5.

The steps of dividing of the polynomial equation by combined factor is noticed below,

Hence, the third zero of the equation is,

x=5.