The roots of the equation 2x^2-3x+5=0 are alpha and beta and the roots of the equation px^2+x+q=0 are alpha-1 and beta-1. Find the value of p and q

2x^2 - 3x + 5 = 0 has roots alpha, beta

alpha + beta = -(-3)/2
=> alpha + beta = 3/2

(alpha)(beta) = 5/2

px^2 + x + q = 0 has roots (alpha - 1) and (beta - 1). Hence,

(alpha - 1) + (beta - 1) = -1/p
=> alpha + beta - 2 = -1/p

Since we have found alpha + beta = 3/2 above,

=> 3/2 - 2 = -1/p
=> -1/2 = -1/p
=> p = 2

Also, 

(alpha - 1)(beta - 1) = q/p
=> (alpha)(beta) - (alpha) - (beta) + 1 = q/p
=> (alpha)(beta) - (alpha + beta) + 1 = q/p

Using (alpha)(beta) = 5/2, alpha + beta = 3/2, and p = 2

=> 5/2 - 3/2 + 1 = q/2
=> 2 = q/2
=> q = 4

Hence, p = 2 and q = 4.