ROOTS AND COEFFICIENTS - PUNJAB-CURRICULUM-AND-TEXTBOOK-BOARD-PCTB / 10TH-CLASS / MATHEMATICS / MATHEMATICS-10-10TH-CLASS-NBF-2024 / QUADRATIC-EQUATIONS / ROOTS-AND-COEFFICIENTS

Let $S_{1}, S_{2}$ be the roots of $ax^{2} + bx + c = 0$ , then using the quadratic formula:

S_{1} = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}, S_{2} = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}

S u m o f r o o t s = S_{1} + S_{2} = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a} + \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}

= \frac{- 2 b}{2 a} = \frac{- b}{a}

a n d p r o d u c t o f r o o t s = S_{1} S_{2} = (\frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}) (\frac{- b - \sqrt{b^{2} - 4 a c}}{2 a})