Question

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

Answer 1

x² − (m + 1) x + 6 = 0

Step 1: Substitute x = 3 into the equation

3² − (m + 1) (3) + 6 = 0

9 − 3(m + 1) + 6 = 0

9 − 3m − 3 + 6 = 0

12 − 3m = 0

3m = 12 ⇒ m = 4

Step 2: Find the second root

x² − (4 + 1) x + 6 = 0 ⇒ x² − 5x + 6 = 0

x² − 5x + 6 = (x − 3) (x − 2) = 0

The roots are: x = 3 and x = 2

m = 4, Roots: x = 3 and x = 2