ROOTS AND COEFFICIENTS OF QUADRATIC EQUATION - PUNJAB-BOARD / 10TH-CLASS / MATHEMATICS / 1-10-MATHS-FULL-10TH-CLASS-NBF-2024 / THEORY-OF-QUADRATIC-EQUATIONS / ROOTS-AND-COEFFICIENTS-OF-QUADRATIC-EQUATION

We know that $\frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$

$\frac{- b + b ^{2} - 4 a c}{2 a}$

and $\frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$

$\frac{- b - b ^{2} - 4 a c}{2 a}$

are roots of the equation $ax^{2} + bx + c = 0$ where $a,b$ are coefficients of $x^{2}$ and $x$ respectively. While $c$ is the constant term.

If $α = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$

$α = \frac{- b + b ^{2} - 4 a c}{2 a}$

and $β = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$

$β = \frac{- b - b ^{2} - 4 a c}{2 a}$

then we can find the sum and the product of the roots as follows.

Sum of the roots $= α + β$

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

Product of the roots $= α β$