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MCQ
Which of the following equations has no real roots?
Options
`x^2 - 4x + 3sqrt(2)` = 0
`x^2 + 4x - 3sqrt(2)` = 0
`x^2 - 4x - 3sqrt(2)` = 0
`3x^2 + 4sqrt(3)x + 4` = 0
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Solution
`x^2 - 4x + 3sqrt(2)` = 0
Explanation:
The given equation is `x^2 - 4x + 3sqrt(2)` = 0.
On coming with `ax^2 + bx + c` = 0
We get `a = 1, b = -4` and `c = 3sqrt(2)`
The discriminant of `x^2 - 4x + 3sqrt(2)` = 0 is
`D = b^2 - 4ac`
= `(-4)^2 - 4(1)(3sqrt(2))`
= `16 - 12sqrt(12)`
= `16 - 12 xx (1.41)`
= `16 - 16.92`
= `- 0.92`
⇒ `b^2 - 4ac < 0`
Concept: Nature of Roots of a Quadratic Equation
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