If the sum of the roots of the equation (x - p)(2x + ...
If the sum of the roots of the equation (x - p)(2x + 1) = 0 is 1, find the value of x
112
12
-32
-112
Correct answer is A
(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 - (2p−1)2x - p2 = 0
compare to x2 - (sum of roots)x + product of roots = 0
sum of roots = 2p−12
But sum of roots = 1
Given; 2p−12 = 1
2p - 1 = 2 x 1
2p - 1 = 2
2p = 2 + 1 = 3
p = 32
p = 112