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Question
Solve the following quadratic equation:
100x2 – 20x + 1 = 0
Sum
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Solution
We write, –20x = –10x – 10x as 100x2 × 1 = 100x2 = (–10x) × (–10x)
∴ 100x2 – 20x + 1 = 0
⇒ 100x2 – 10x – 10x + 1
⇒ 10x(10x – 1) – 1(10x – 1) = 0
⇒ (10x – 1) (10x – 1) = 0
⇒ (10x – 1)2 = 0
⇒ 10x – 1 = 0
⇒ `x = 1/10`
Hence, `1/10` is the repeated root of the given equation.
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