Question

The discriminant of the quadratic equation \( x - \frac{1}{x} = 1 \) will be:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

The discriminant of a quadratic equation determines the nature of its roots: if \( \Delta>0 \), the roots are real and distinct, if \( \Delta = 0 \), the roots are real and equal, and if \( \Delta<0 \), the roots are complex.

Answer 1

The Correct Option is C

Step 1: Express the given equation in standard form.
Start with the equation: \[ x - \frac{1}{x} = 1 \] Multiply through by \(x\) to clear the denominator: \[ x^2 - 1 = x \] Rearrange it into standard quadratic form: \[ x^2 - x - 1 = 0 \]
Step 2: Use the quadratic formula to find the discriminant.
The discriminant \( \Delta \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by: \[ \Delta = b^2 - 4ac \] For the equation \( x^2 - x - 1 = 0 \), we have \(a = 1\), \(b = -1\), and \(c = -1\). Therefore, the discriminant is: \[ \Delta = (-1)^2 - 4(1)(-1) = 1 + 4 = 5 \] Thus, the discriminant is 5. Therefore, the correct answer is (D).