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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 - Mathematics

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

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Solution

`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.

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