Question

Roots of the equation x4 - 2x3 – 5x2 - 7x+10=o are a, Bord and that of x4 + 3 + bx2 +cx+d = 0 be
« + B+ y, a +8+8,2+7+8; B+ 7+8, then find the value of a +b-c-d.​

Answer 1

Answer:

Step-by-step explanation:

We are given that polynomial (x4+ax3-7x2+8x+b) is exactly divisible by (x+2) as well as (x+3).

The two divisors in the question are (x + 2) and (x + 3). As it is given that the given polynomial is divisible by both these divisors, that means;

x + 2 = 0   and   x + 3 = 0

x = -2  and  x = -3 will make the remainder zero when these values of x are substituted in the given polynomial.

f(x) = . So, f(-2) and f(-3) will be equal to zero.

f(-2) =

f(-3) =

f(-2) =

      =   ---------------- [Equation 1]

f(-3) =

     =    ---------------- [Equation 2]

Now using the elimination method to find the values of a and b;

                   

                   

                   +        -     +       -  

                        19a - 22 = 0

                           a =

Putting the value of a in equation 1 we get;

                         

                         

                            b  =  

                            b  =   .

Hence, the value of a =   and the value of b =  .[/tex]

Step-by-step explanation: