Question

If quadratic equation `x^2 – (m + 1) x + 6 = 0 `has one root as x = 3; find the value of m and the other root of the equation.  

Answer 1

`x^2 – (m + 1)x + 6 = 0`
Put x = 3 in the given equation
`(3)^2 – (m + 1) (3) + 6 = 0`
⟹ `9 – 3m – 3 + 6 = 0`
⟹ `– 3m = – 12`
⟹ `m = 4` 

Put this value of m in the given equation, we get 

`x^2 – 5x + 6 = 0`
⟹ `x^2 – 3x – 2x + 6 = 0`
⟹ `x(x – 3) – 2(x – 3) = 0`
⟹ `(x – 3) (x – 2) = 0`
If` x – 3 = 0  "Or"  x – 2 = 0`
Then `x = 3  "Or"  x = 2`
∴ 2 is the other root of the given equation