If `x=1 a n d x=2` are solutions of equations `x^3+a x^2+b x+c=0a n da+b=1,` then find the value of `bdot`

Answer

` b= 5`

Explanation

Since x = 1 is a root of the given equation, it satisfiles the equation.
Hnece, putting x = 1 in the given equation, we get
`a + b + c = 1 (1)`
but given that
`a + b = 1 `
`rArr c = -2` (2)
Now put x = 2 in the given equation, we have
` 8 + 4a + 2b - 2 = 0`
or `6 + 2a + 2 (a + b) = 0`
or ` 6 + 2a + 2 = 0`
or `a = -4`
`rArr b = 5`