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The quadratic equation 2x2-5x+1 = 0 has ______ - Mathematics

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MCQ
Fill in the Blanks

The quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has ______.

Options

  • Two distinct real roots

  • Two equal real roots

  • No real roots

  • More than 2 real roots

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Solution

The quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has no real roots.

Explanation:

Given equation is `2x^2 - sqrt(5)x + 1` = 0

On comapring with `ax^2 + bx + c` = 0

We get `a = 2, b = - sqrt(5)` and c = 1

∴ Discriminant, `D = b^2 - 4ac = (-sqrt(5))^2 - 4 xx (2) xx (1) = 5 - 8`

= `- 3 < 0`

Since, discrimant is negative

Therefore quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has no real roots

i.e. imaginary roots.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 8 | Page 37
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