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Question
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
Solution
5x2 – 8x – 4 = 0
∵ 5 × ( – 4) = – 20
-20 = – 10 + 2
-8 = – 10 + 2
⇒ 5x2 - 10x + 2x - 4 = 0
⇒ 5x(x - 2) + 2(x - 2) = 0
⇒ (x - 2) (5x + 2) = 0 ...(Zero Product Rule)
Either x - 2 = 0,
then x = 2
or
5x + 2 = 0,
then 5x = -2
⇒ x = `-(2)/(5)`
∴ x = 2, `-(2)/(5)`.
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