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Which of the following equations has no real roots? - Mathematics

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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
  Is there an error in this question or solution?

APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 10 | Page 37
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