Question

Find the nature of the roots of equation x-1/x=1
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Answer 1

Required Answer:-

Given:

• x - 1/x = 1

To find:

• The nature of roots of the given equation.

Solution:

We have,

➡ x - 1/x = 1

➡ (x² - 1)/x = 1

➡ x² - 1 = x

➡ x² - x - 1 = 0

The discriminant of a quadratic equation tells the nature of roots. Three cases arises here.

• If discriminant is greater than 0, then roots are real and different.
• If discriminant is equal to 0, then roots are equal.
• If discriminant is less than 0, then roots are imaginary.

Here,

➡ a = 1 (coefficient of x²)

➡ b = -1 (coefficient of x)

➡c = -1 (coefficient of x⁰)

So, discriminant will be,

= b² - 4ac

= 1² - 4 × (1) × (-1)

= 1 + 4

= 5

★ As the discriminant is greater than 0, the roots of the given equation are real and unequal.

Answer:

• The roots if the given equation are real and unequal.

Answer 2

Step-by-step explanation:

Given:

x - 1/x = 1

To find:

The nature of roots of the given equation.

Solution:

We have,

➡ x - 1/x = 1

➡ (x² - 1)/x = 1

➡ x² - 1 = x

➡ x² - x - 1 = 0

The discriminant of a quadratic equation tells the nature of roots. Three cases arises here.

If discriminant is greater than 0, then roots are real and different.

If discriminant is equal to 0, then roots are equal.

If discriminant is less than 0, then roots are imaginary.

Here,

➡ a = 1 (coefficient of x²)

➡ b = -1 (coefficient of x)

➡c = -1 (coefficient of x⁰)

So, discriminant will be,

= b² - 4ac

= 1² - 4 × (1) × (-1)

= 1 + 4

= 5

★ As the discriminant is greater than 0, the roots of the given equation are real and unequal.

Answer:

The roots if the given equation are real and unequal.