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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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