2=kx^2+x

kx^2+x-2=0

1^2-4k*(-2)

= 1+8k is greater than or equal to 0.

8k ≥ - 1

K is greater than or equal to-1/8.

Because the principle of thermometer is that the height of scale line is linear with temperature, let the real temperature of A (the index of B) be X, the apparent temperature (the index of A) be Y, and the correlation coefficients be A and B; Then X=a*Y+b

Substitute the question meaning condition: 20 = a *15+b;

80=a*78+b

The simultaneous equations are solved as follows: a=60/63=20/2 1, b=40/7.

Then, the relationship between x and y is: x = 20/21* y+40/7 ... (1).

When the index of A is -2, the index of B is: x = 20/21* (2)+40/7 = 80/21= 3.8 degrees.

Let the indexes of a and b be the same, and the temperature is x.

Then x=20x/2 1+40/7.

2 1x=20x+ 120

x= 120

Then when the temperature is 120, the indication is the same.