If the sum of the roots of the equation (x – p)(2x – 1) – 0 is 1, find the value of x
-
A.
1(frac{1}{2}) -
B.
(frac{1}{2}) -
C.
-(frac{3}{2}) -
D.
-1(frac{1}{2})
Correct Answer: Option A
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})