Monoxdifly
MHB
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The equation $$(a-1)x^2-4ax+4a+7=0$$ with a is a whole number has positive roots. If $$x_1>x_2$$ then $$x_2-x_1=...$$
A. –8
B. –5
C. –2
D. 2
E. 8
Since the equation has positive roots then $$x_1>0$$ and $$x_2>0$$ thus $$x_1+x_2>0$$ and $$x_1x_2>0$$
$$x_1+x_2>0$$
$$\frac{-(-4a)}{a-1}>0$$
$$x_1x_2>0$$
$$\frac{4a+7}{a-1}>0$$
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.
A. –8
B. –5
C. –2
D. 2
E. 8
Since the equation has positive roots then $$x_1>0$$ and $$x_2>0$$ thus $$x_1+x_2>0$$ and $$x_1x_2>0$$
$$x_1+x_2>0$$
$$\frac{-(-4a)}{a-1}>0$$
$$x_1x_2>0$$
$$\frac{4a+7}{a-1}>0$$
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.