Question

Let ( x(square)+ 3x +1) over (2 x(square) -5x+2) = k ----------be y

1) Express y in the form of a x(square) + bx +c =0

2) If -3/4 is a root of y, find the value of k

Answer 1

it's much easier to write

(x^2+3x+1)/(2x^2-5x+2) = k
x^2+3x+1 = 2kx^2 - 10kx+2k
(1-2k)x^2 + (3+10k)x + (1-2k) = 0

since -3/4 is a root,

(1-2k)(9/16) + (3+10k)(-3/4) + (1-2k) = 0
-1/16 (170k+11) = 0
k = -11/170