Question

find the zeroes of the polenomial x²-4x+3​

Answer 1

$\begin{gathered} {x}^{2} - 4x + 3 = 0 \\ \\ {x}^{2} - x - 3x + 3 = 0 \\ \\ x(x - 1) - 3(x - 1) = 0 \\ \\ (x - 1) \: (x - 3) = 0 \\ \\ x = 1 \: \: \: and \: \: x = 3\end{gathered}$

Sum of roots :-

$\begin{gathered} \alpha + \beta = 1 + 3 \\ \\ = 4 = \frac{ - ( - 4)}{1} = \frac{ - b}{a} \end{gathered}$

Product of roots :-

$\begin{gathered} \alpha \times \beta = 1 \times 3 \\ = 3 = \frac{3}{1} = \frac{c}{a} \end{gathered}$