Use the given curve y = x²/3 − 1/(2x) on the grid to find, by drawing a suitable straight line, estimates to 1 decimal place of the roots of 4x³ + 3x² − 36x − 6 = 0 for −4

Question

Use the given curve y = x²/3 − 1/(2x) on the grid to find, by drawing a suitable straight line, estimates to 1 decimal place of the roots of 4x³ + 3x² − 36x − 6 = 0 for −4 < x < 0.

Accepted Answer

Divide 4x³ + 3x² − 36x − 6 = 0 by 12x: x²/3 + x/4 − 3 − 1/(2x) = 0 So x²/3 − 1/(2x) = 3 − x/4 Draw the line y = 3 − x/4 (through (0, 3) and (−4, 4)) Read the x-coordinates where the line meets the curve: x = −0.2 and x = −3.3 Answer: x = −0.2 and x = −3.3 (or −3.4)

4PM1/02 Jun 2024, Question 4: Solving Equations by Graphical Methods

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