If quadratic equation x2 – (m + 1) x + 6 = 0 has one root as x = 3;

1.	If quadratic equation x2 – (m + 1) x + 6 = 0 has one root as x = 3; find the value of m and the other root of the equation.
Answer» x²– (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 x² – 5x + 6 = 0 ⟹ x² – 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

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

Answer»

x²– (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

x² – 5x + 6 = 0

⟹ x² – 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