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Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Solution
The equation `(x - sqrt(2))^2 - 2(x + 1)` = 0 has two distinct and real roots.
Simplifying the above equation,
`x^2 - 2sqrt(2)x + 2 - sqrt(2)x - sqrt(2)` = 0
`x^2 - sqrt(2)(2 + 1)x + (2 - sqrt(2))` = 0
`x^2 - 3sqrt(2)x + (2 - sqrt(2))` = 0
D = b2 – 4ac
= `(- 3sqrt(2))^2 - 4(1)(2 - sqrt(2))`
= `18 - 8 + 4sqrt(2) > 0`
Hence, the roots are real and distinct.
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