Answer: The sum of roots of the polynomial is 8.
Explanation:
The given polynomial is,
[tex]f(x)=x^3-8x^2-23x+30[/tex]
Use hit and trial method to find the one root. Since [tex]\pm1[/tex] is the possible rational root for each polynomial.
[tex]f(1)=(1)^3-8(1)^2-23(1)+30=0[/tex]
Sicen at x=1 the value of f(x) is 0 therefore 1 is a root of the polynomial and (x-1) is a factor of the polynomial.
Use synthetic division or long division method to find the other factor of the polynomial.
[tex]f(x)=x^3-8x^2-23x+30=(x-1)(x^2-7x-30)[/tex]
[tex]f(x)=(x-1)(x^2-10x+3x-30)[/tex]
[tex]f(x)=(x-1)(x(x-10)+3(x-10))[/tex]
[tex]f(x)=(x-1)(x-10)(x+3)[/tex]
Equation each factor of f(x) equal to 0.
[tex]x=-3,1,10[/tex]
So, the roots are -3, 1, 10. Sum of roots is,
[tex]-3+1+10=8[/tex]
Therefore, the sum of roots of the polynomial is 8.
