Question

1. If the following quadratic equation has one root as x = 3; find the value
of m and the other root of the equation.
x2 – (m + 1) x + 6 = 0​

Answer 1

x² – ( m + 1 )x + 6 = 0

Given one root is x = 3

Therefore putting it in above quadratic equation.

(3)² – ( m + 1 )(3) + 6 = 0

9 – 3m – 3 + 6 = 0

–3m + 12 = 0

– 3m = – 12

3m = 12

m = 12 / 3

m = 4

So the quadratic equation is

x² – ( 4 + 1 )x + 6 = 0

x² – 5x + 6 = 0

x² – 3x – 2x + 6 = 0

x ( x – 3 ) – 2 ( x – 3 ) = 0

( x – 3 ) ( x – 2 ) = 0

x – 3 = 0

x = 3

x – 2 = 0

x = 2

Hence, its other root is 2

Hope the solution is clear to you!!