If the sum of the roots of the equation (x - p)(2x - 1) -

Explanation

(x - p)(2x + 1) = 0

2x² + x - 2px - p = 0

2x² + x (1 - 2p) - p = 0

2x² - (2p - 1)x - p = 0

divide through by 2

x² - \(\frac{(2p - 1)}{2}\)x - \(\frac{p}{2}\) = 0

compare to x² - (sum of roots)x + product of roots = 0

sum of roots = \(\frac{2p - 1}{2}\)

But sum of roots = 1

Given; \(\frac{2p - 1}{2}\) = 1

2p - 1 = 2 x 1

2p - 1 = 2

2p = 2 + 1 = 3

p = \(\frac{3}{2}\)

p = 1\(\frac{1}{2}\)