Question

Let g(x) = x^2 + bx + c. If g(2) = 0
and g(-3) = 0, find b + c.

Answer 1

`b+c-5`

Explanation:

The given function is
`g(x)=x^2+bx+c`

If g(2)=0, then we can substitute x=2 and g(x)=0 to get:

`0=2^2+2b+c`

`0=4+2b+c`

`2b+c=-4`...(1)

Also g(-3)=0

`\implies (-3)^2+b(-3)+c=0`

`\implies 9-3b+c=0`

`\implies -3b+c=-9`...(2)

Equation (1) - equation (2) gives

`2b--3b=-4--9`

`5b=5`

b=1

Put b=1 into equation 1

`2(1)+c=-4`

`2+c=-4`

`c=-4-2=-6`

Therefore
`b+c=1+-6=-5`