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Solve: `6x^(2)-x-2=0` by the factorisation method.

Answer» We write, `-x=-4x+3x` as `(-4x)xx3x=-12x^(2)=6x^(2)xx(-2).`
`:." "6x^(2)-x-2=0`
`implies" "6x^(2)-4x+3x-2=0implies2x(3x-2)+(3x-2)=0`
`implies" "(3x-2)(2x+1)=0implies3x-2=0" or "2x+1=0`
`implies" "x=(2)/(3)" or "x=(-1)/(2).`
Hence, `(2)/(3)` and `(-1)/(2)` are the roots of the given equation.


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