Answer:
[tex]b+c-5[/tex]
Step-by-step explanation:
The given function is [tex]g(x)=x^2+bx+c[/tex]
If g(2)=0, then we can substitute x=2 and g(x)=0 to get:
[tex]0=2^2+2b+c[/tex]
[tex]0=4+2b+c[/tex]
[tex]2b+c=-4[/tex]...(1)
Also g(-3)=0
[tex]\implies (-3)^2+b(-3)+c=0[/tex]
[tex]\implies 9-3b+c=0[/tex]
[tex]\implies -3b+c=-9[/tex]...(2)
Equation (1) - equation (2) gives
[tex]2b--3b=-4--9[/tex]
[tex]5b=5[/tex]
b=1
Put b=1 into equation 1
[tex]2(1)+c=-4[/tex]
[tex]2+c=-4[/tex]
[tex]c=-4-2=-6[/tex]
Therefore [tex]b+c=1+-6=-5[/tex]
