(x - 3)(x - p) = p(1 - x) has equal roots. The value of p is

(A) 8/9 (B) 9/8 (C) 4/9 (D) -9/4

Please explain.

x^2-(p+3)x+3p-p+px = 0
x^2-3x+2p = 0
b^2 = 4ac for equal roots
9 = 8p
p = 9/8
Answer (B)

B 9/8

Expand (x - 3)(x - p) = x^2 -3x- px +3p

Expand p(1 - x) = p - px

Equate these two x^2 -3x- px +3p = p - px

x^2 -3x -px +3p -p +px =0

x^2 -3x +2p = 0

This equals (x-k)^2

so k^2 = 2p and -2k = -3 so k = 3/2 therefore 9/4 =2p so p=9/8

x^2 -px - 3x + 3p = p - px
x^2 -3x + 3p = 0


x = [- b + or - square root(b^2 -4*a*c)]/2a
If roots are equal then (b^2 - 4*a*c must = 0
if roots are equal then (-3)^2 = 4*1*3p
9 = 12p
p = 3/4