[ASK] Stuck on a Quadratic Equation

[Monox D. I-Fly]

The equation [tex](a-1)x^2-4ax+4a+7=0[/tex] with a is a whole number has positive roots. If [tex]x_1>x_2[/tex] then [tex]x_2-x_1=...[/tex]

A. –8

B. –5

C. –2

D. 2

E. 8


Since the equation has positive roots then [tex]x_1>0[/tex] and [tex]x_2>0[/tex] thus [tex]x_1+x_2>0[/tex] and [tex]x_1x_2>0[/tex]


[tex]x_1+x_2>0[/tex]

[tex]\frac{-(-4a)}{a-1}>0[/tex]


[tex]x_1x_2>0[/tex]

[tex]\frac{4a+7}{a-1}>0[/tex]


However I progressed, I couldn't determine a as a single value and only found it as a set of certain whole numbers. Can you help me to find the single value of a? Once I know that. I guess I can continue on my own.

[Guest]

The problem does NOT ask you to find a! It asks you to find [tex]x_2- x_1[/tex], Further, since it specifically says that [tex]x_1> x_1[/tex], [tex]x_2- x_1[/tex] must be negative, one of A, B, or C. Use the fact that a> -7/4 to determine which [tex]x_2- x_1[/tex] must be.