The equation 3^3-10x+9=0 has a zero in the interval [-3,-2]. Use the intermediate value theorem to approximate the solution correct to two decimal places.
+53 Simplifying
x3 + -10x + 9 = 0
Reorder the terms:
9 + -10x + x3 = 0
Solving 9 + -10x + x3 = 0
Solving for variable 'x'. The solution to this equation could not be determined.
+33614 y = x3 - 10x + 9 doesn't have a zero in the interval [-3, -2]! It has a zero in the interval [-4, -3].
When x = -4 we have y = -15. When x = -3 we have y = 12, so the signs are different at each end of the interval.
What about half way at x = -3.5? Here y = 1.125. This is positive so the solution lies in the interval [-4, -3.5]
Now try half way in this interval, I.e. x = -3.75. Here y ≈ -6.2344. This is negative, so the solution must lie in the interval [-3.75, -3.5].
Continue in this way until you find the value of x that is the same to within two decimal places on successive estimates.
(You should find x = -3.54 to two dp)
