If f(x) = x^3 + 8x² + 11x-20 and x+5 is a factor of f(x), then find all of the zeros of f(x) algebraically

The zeros are (-5,-4,-1)

Step-by-step explanation:

Since we have a linear factor, we can use the method of long division to get the other factors

What this mean is that we simply divide the polynomial by the linear expression

we have this division result as;

By dividing, we have the other factor as ;

x^2 + 3x - 4

so we simply factorize this

x^2 -x + 4x - 4

x(x-1) + 4(x-1)

(x + 4)(x-1)

So the complete factors are;

(x + 5)(x + 4)(x-1)

To get the zeros, we simply equate each of the terms to zero

and we have our answer as;

-5 , -4 , 1

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y