Question

Solve the following quadratic equation by factorization.

`2"x"^2 - 2"x" + 1/2 = 0`

Answer 1

`2"x"^2 - 2"x" + 1/2 = 0`

∴ `2 xx 2"x"^2 - 2 xx 2"x" + 2 xx 1/2 = 2 xx 0` ....[Multiplying both sides by 2]

∴ 4x² − 4x + 1 = 0 .....`[(-2 xx -2),(-2-2)] = +4`

∴ 4x² − 2x − 2x + 1 = 0

∴ 2x(2x − 1) − 1(2x − 1) = 0

∴ (2x − 1) (2x − 1) = 0

∴ 2x − 1 = 0 or 2x − 1 = 0

∴ 2x = 1 or 2x = 1

∴ x = `1/2` or x = `1/2`

∴ `1/2` and `1/2` are the roots of the given quadratic equation.