Question

given that 2 and k are roots of the quadratic equation (x+4) (x-p) = (2-x). find the values of k and p

Answer 1

The roots of the equation are 2 and k
substituting x=2 in the equation
(x+4)(x-p) = 2-x
(2+4)(2-p) = 2-2
6(2-p) = 0
dividing 6 both side, the answer is
p = 2

substituting x in the equation we 
(x-4)(x-p) = 2-x
x² - 2x + 4x- 8 = 2-x
x² - 2x + 4x -8 -2 -x = 0
x² + 3x - 10 = 0
x² + 5x -2x - 10 = 0
x(x + 5) -2( x + 5) = 0
(x + 5)( x - 2) =0
(x + 5) = 0 or (x - 2) = 0
x = -5 and x = 2
therefor k = -5 and p = 2