= gives x and x – = gives x = . x and x = are the solutions of the equation. In other words, and are the roots of the equation x – x + = . Verify that these are the roots of the given equation.
Note that we have found the roots of x – x + = by factorising x – x + into two linear factors and equating each factor to zero . Example : Find the roots of the quadratic equation x – x – = . Solution : We have x – x – = x + x – x – = x ( x + ) – ( x + ) = ( x – )( x + ) The roots of x – x – = are the values of x for which ( x – )( x + ) = Therefore, x – = or x + = , x = or x = Therefore, the roots of x – x – = are . and – We verify the roots, by checking that and satisfy x – x – = .
Example : Find the roots of the quadratic equation Solution : = =