If the nonzero real number A.B.C is known to be an arithmetic sequence, then the number of intersections between the image and the x-axis of the quadratic function f (x) = ax ^ 2 + 2bx + C / 4

a. B. C into arithmetic sequence
2b=a+c
4b^2-4a*c/4
=4b^2-ac
=4(a+c)^2-ac
=4a^2+7ac+4c^2
=(2a+7c/4)^2+17c^2/16
>0
Therefore, there are two intersections between the image and the X axis

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