Question

Find the value of p for which the quadratic equation 2x² + px + 8 = 0 has real roots.

Answer 1

Given: 

2x² + px + 8 = 0

Here, 

a = 2, b = p and c = 8 

Discriminant D is given by: 

D = (b² – 4ac)

= p² – 4 × 2 × 8 

= (p² – 64)  

If D > 0, the roots of the equation will be real 

⇒ (p² – 64) ≥ 0 

⇒ (p + 8) (p – 8) ≥ 0 

⇒ p ≥ 8 and p ≤ –8 

Thus, the roots of the equation are real for p ≥ 8 and p ≤ –8.