Question

(x² + 1)² – x² = 0 has
(a) four real roots
(b) two real roots
(c) no real roots
(d) one real root

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Answer 1

Answer:

(c) no real roots

Explanation:

The Equation has Imaginary Roots, therefore it has 0 Roots.

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Answer 2

(x² + 1)² – x² = 0 has no real roots

Given :

The equation (x² + 1)² – x² = 0

To find :

(x² + 1)² – x² = 0 has

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real root

Solution :

Step 1 of 4 :

Write down the given equation

The given equation is

(x² + 1)² – x² = 0

Step 2 of 4 :

Simplify the given equation

(x² + 1)² - x² = 0

⇒ x⁴ + 2x² + 1 - x² = 0

⇒ x⁴ + x² + 1 = 0

Step 3 of 4 :

Find Discriminant of the equation

Let y = x²

Then above equation becomes

x⁴ + x² + 1 = 0

⇒ y² + y + 1 = 0

Comparing with the general equation

ay² + by + c = 0 we get

a = 1 , b = 1 and c = 1

Discriminant

= b² - 4ac

= 1² - 4 × 1 × 1

= 1 - 4

= - 3

Step 4 of 4 :

Find number of real roots of the equation

Discriminant

= b² - 4ac

= - 3 < 0

So the equation has no real roots.

Hence the correct option is (c) no real roots

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