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PGCIL DT Electrical 13 Aug 2021 Official Paper (NR I)

Option 2 : 2

__Concept:__

Let us consider the standard form of a quadratic equation, ax2 + bx + c = 0

Let α and β be the two roots of the above quadratic equation.

1. The sum of the roots of a quadratic equation are: α + β = (-b/a)$\alpha +\beta =-\frac{\mathrm{b}}{\mathrm{a}}=-\frac{(\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\text{}\mathrm{o}\mathrm{f}\text{}\mathrm{x})}{(\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\text{}\mathrm{o}\mathrm{f}\text{}{\mathrm{x}}^{2})}$

2. The product of the roots is given by: α × β = (c/a)

__Calculation:__

The given equation is x^{2} + px + q = 0

$\frac{1}{\alpha}$

⇒ 2 + 4 = (-p)

⇒ p = -6

again, 2 × 4 = (q)

⇒ q = 8

∴ Required sum = 8 + (-6) = 2