Answer:
1.7.
Explanation:
2x^3 + 9x^2 - 2x + 8 = 40
Substituting values for x in the range 1 to 2:
when x = (1.1):
f(1.1) = 2(1.1)^3 + 9(1.1)^2 - 2(1.1) + 8 = 19.32.
x = 1.3:
f(1.3) = 25.004
F(1.5) = 32
F(1.6) = 36.032
F(1.7) = 40.436 which is just greater than 40.
So the root is between 1.6 and 1.7.
f(1.65) = 38.19
Therefore the root is > 1.65 and < 1.7
and to 1 DP it is 1.7.