Question

For what value of p is the coefficient of x² in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ?

Answer 1

(2x – 1) (x – k) (px + 1) = (2x – 1) (px² + x – kpx – k) 

= 2px³ + 2x² – 2kpx² – 2kx – px² – x + kpx + k 

= 2px³ + \(x\)² [2 – 2kp – p] – \(x\) [2k + 1 – kp] + k 

Here constant term = k = 2. 

Coefficient of x² = 2 – 2kp – p = 2 – 4p – p = 2 – 5p 

Given, 2 – 5p = 0 ⇒ p = \(\frac{2}{5}\) .