F.4 Amath -Quardratic Equation

a)(x^2+3x+1)/(2x^2-5x+2)=L
(x^2+3x+1) = L(2x^2-5x+2)
(x^2+3x+1) = 2Lx^2-5Lx+2L
(2L - 1)x^2 - (5L+3)x + 2L-1 = 0
sub x= -3/4 to the result of a) :
(-3/4)^2 * (2L-1) - (-3/4)(5L+3) + 2L-1 = 0
(9/8)L - 9/16 + (15/4)L+ 9/4 + 2L-1 = 0
18L - 9 + 60L + 36 + 32L - 16 = 0
110L = - 11
L = - 1 / 10
c) Let the other root be B , then
(-3/4)B = (2L-1)/(2L-1)
(-3/4)B = 1
B = - 4/3







2009-03-15 22:09:09 補充：
兩根之積 = C/A, C同A都 = 2L - 1 。