Question

If the roots of the quadratic equation x2 - kx + 4 = 0 are equal, then find the value of 'k'.

1. ± 3
2. ± 4
3. ± 2
4. 0
5. None of these

Answer 1

Correct Answer - Option 2 : ± 4

Concept:

Let us consider the standard form of a quadratic equation, ax2 + bx + c = 0

Discriminant = D = b2 – 4ac

• If the Discriminant > 0 then the roots are real and distinct.
• If the Discriminant = 0 then the roots are real and equal.
• If the Discriminant < 0 then the roots are Imaginary.

Calculation:

Given:

The roots of the quadratic equation x2 - kx + 4 = 0 are equal.

For equal roots, Discriminant = 0

⇒ D = b2 – 4ac = 0

⇒ (-k)² - 4 × 1 × 4 = 0

⇒ k² - 16 = 0

⇒ k2 = 16

∴ k = ± 4