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(x2 + 1)2 – x2 = 0 has ______. - Mathematics

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MCQ
Fill in the Blanks

(x2 + 1)2 – x2 = 0 has ______.

Options

  • Four real roots

  • Two real roots

  • No real roots

  • One real root

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Solution

(x2 + 1)2 – x2 = 0 has no real roots.

Explanation:

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

⇒ `x^4 + 1 + 2x^2 - x^2 = 0`  ......`[because (a + b)^2 = a^2 + b^2 + 2ab]`

⇒ `x^4 + x^2 + 1` = 0

Let `x^2 = y`

∴ `(x^2)^2 + x^2 + 1` = 0

`y^2 + y + 1` = 0

On comparing with `ay^2 + by + c` = 0

We get a = 1, b = 1 and c = 1

Discriminant, D = b2 – 4ac

= `(1)^2 - 4(1)(1)`

= `1 - 4`

= `-3`

Since, D < 0

∴ `y^2 + y + 1` = 0

i.e., `x^4 + x^2 + 1` = 0

or `(x^2 + 1)^2 - x^2` = 0 has no real roots.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 11 | Page 38
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