1.6: Solve cubic equations using a graph

4PM1/1/November/2020 — Question 4 · 7 marks

1.6 diagram 1
Figure 2 shows the graph of
y=x+5x2y=x+\frac{5}{x^2}
for 1x4\displaystyle 1\leq x\leq4, drawn on a grid.
(a) By drawing a suitable straight line on the grid, obtain estimates, to one decimal place, for the roots of
x34x2+5=0x^3-4x^2+5=0
in the interval 1x4\displaystyle 1\leq x\leq4.
(3)
(b) By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, for the root of
x3x25=0x^3-x^2-5=0
in the interval 1x4\displaystyle 1\leq x\leq4.
(4)