Question

If -5 is a root of the quadratic equation 2x² + px - 15 = 0 and also of the quadratic equation p(kx² + x) = 0, then what are the values of p and k?
1. 7, 0.2
2. -7, 0.4
3. 7, -0.2
4. -7, -0.2

Answer 1

Correct Answer - Option 1 : 7, 0.2

Given:

Root of equations 2x2 + px - 15 = 0 & p(kx2 + x) = 0 = - 5 

Calcultion:

By putting x = - 5 in 2x2 + px - 15 = 0 

⇒ 2(- 5)² + p × - 5 - 15 = 0 

⇒ 50 - 5p - 15 = 0 

⇒ - 5p = - 35 

∴ p = 7 

By putting x = - 5 and p = 7 in equation p(kx2 + x) = 0

⇒ 7(k × (- 5)² + (- 5)) = 0 

⇒ 175k - 35 = 0

⇒ k = 35/175

⇒ k = 1/5

∴  k = 0.2

Hence, the values of p = 7 and k = 0.2.