It is known that two X 1 and x 2 of the quadratic equation AX2 + BX + C = 0 satisfy x 2 / x 1 + x 1 / x 2 = 14 / 5, and the image of the inverse scale function y = A / X intersects the symmetric axis of the parabola y = AX2 + BX + C at the point (6, - 1 / 12)

It is known that two X 1 and x 2 of the quadratic equation AX2 + BX + C = 0 satisfy x 2 / x 1 + x 1 / x 2 = 14 / 5, and the image of the inverse scale function y = A / X intersects the symmetric axis of the parabola y = AX2 + BX + C at the point (6, - 1 / 12)

x2/x1+x1/x2=14/5
(x1^2+x2^2)/(x1x2)=14/5
(x1+x2)^2/(x1x2)-2=14/5
(b^2/a^2)/(c/a)=24/5
b^2/(ac)=24/5
Axis of symmetry - B / 2A = 6,12a + B = 0
There is a point (6, - 1 / 12) on y = A / X,
-1 / 12 = A / 6, a = - 1 / 2,
b=6,
c=-15
y=-1/2*x^2+6x-15