Question

Find the values of k for which the given quadratic equation has real and distinct roots:  

5x² – kx + 1 = 0

Answer 1

The given equation is 5x² – kx + 1 = 0 

∴ D = (–k)² – 4 × 5 × 1

= k² – 20  

The given equation has real and distinct roots if D > 0 

∴ k² – 20 > 0 

⇒ `k^2 - (2sqrt(5))^2 > 0` 

⇒ `(k - 2sqrt(5)) (k + 2sqrt(5)) > 0` 

⇒ `k < -2sqrt(5) or k > 2sqrt(5)`