1. The problem asks to solve the equation $$2x^3 - 5x = 0$$ by drawing a suitable straight line. 2. First, rewrite the equation as: $$2x^3 - 5x = 0$$ 3. Factor out the common term $x$: $$x(2x^2 - 5) = 0$$ 4. Set each factor equal to zero: - For $x = 0$ - For $2x^2 - 5 = 0$ 5. Solve the quadratic equation: $$2x^2 - 5 = 0 \implies 2x^2 = 5 \implies x^2 = \frac{5}{2} \implies x = \pm \sqrt{\frac{5}{2}}$$ 6. Therefore, the solutions are: $$x = 0, \quad x = \sqrt{\frac{5}{2}}, \quad x = -\sqrt{\frac{5}{2}}$$ 7. In decimal form, approximately: $$x \approx 0, \quad x \approx 1.58, \quad x \approx -1.58$$ 8. The straight line to draw for solving this graphically is $y = 0$, the x-axis, and the intersections of the curve $y = 2x^3 - 5x$ with this line give the roots. Final answer: $$x = 0 \quad \text{or} \quad x = \sqrt{\frac{5}{2}} \quad \text{or} \quad x = -\sqrt{\frac{5}{2}}$$