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Quadratic Solution De0E8B

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Quadratic Solution De0E8B


1. The problem is to solve the equation or understand the content on page 70 of the 1st year Math book Sindh Board as referenced. 2. Since the exact problem is not specified, I will demonstrate solving a typical algebraic problem that might appear on such a page, for example, solving a quadratic equation. 3. The general quadratic equation is given by $$ax^2 + bx + c = 0$$. 4. The solution formula (quadratic formula) is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 5. Important rules: - The discriminant $$\Delta = b^2 - 4ac$$ determines the nature of roots. - If $$\Delta > 0$$, two distinct real roots. - If $$\Delta = 0$$, one real root (repeated). - If $$\Delta < 0$$, two complex roots. 6. Example: Solve $$2x^2 - 4x - 6 = 0$$. 7. Calculate discriminant: $$\Delta = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$. 8. Since $$\Delta = 64 > 0$$, two distinct real roots. 9. Calculate roots: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$. 10. Roots are: $$x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$$, $$x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$. 11. Therefore, the solutions are $$x = 3$$ and $$x = -1$$. 12. This method can be applied to any quadratic equation to find its roots.