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Question
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solution
`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.
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