Question

If –5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.

Answer 1

It is given that –5 is a root of the quadratic equation 2x² + px – 15 = 0  

∴ 2(–5)² + p × (–5) – 15 = 0 

⇒ –5p + 35 = 0  

⇒ p = 7 

The roots of the equation px² + px + k = 0 are equal. 

∴ D = 0 

⇒ p² – 4pk = 0 

⇒ (7)² – 4 × 7 × k = 0 

⇒ 49 – 28k = 0 

⇒ `k = 49/28 = 7/4` 

Thus, the value of k is `7/4`.