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.
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.
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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
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