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Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
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Solution
The equation `sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0 has two real and distinct roots.
D = b2 – 4ac
= `(-3/sqrt(2))^2 - 4(sqrt(2))(1/2)`
= `(9/2) - 2sqrt(2) > 0`
Hence, the roots are real and distinct.
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