Target Mathematics

1.3: Estimate roots using a graph

4PM1/2/June/2024 — Question 4 · 4 marks

1.3 diagram 1
Figure 2 shows part of the curve with equation y=x2312xy = \frac{x^2}{3} - \frac{1}{2x} for 4<x<0-4 < x < 0
By drawing a suitable straight line on the grid, obtain estimates, to one decimal place,
of the roots of the equation 4x3+3x236x6=04x^3 + 3x^2 - 36x - 6 = 0 in the interval 4<x<0-4 < x < 0
(4)