Question

find the root of the following quradatic equation by factorisation 2x2-7x+6​

Answer 1

$\mathtt{p(x) = 2x²-7x+6}$

$\mathtt{\;\;\;\;\;\;\; = 2x²-4x-3x+6}$

$\mathtt{\;\;\;\;\;\;\; = 2x(x-2)-3(x-2)}$

$\mathtt{\;\;\;\;\;\;\; = (x-2)(2x-3)}$

$\mathtt{If \; p(x) = 0}$

$\implies \mathtt{(x-2)(2x-3) = 0}$

$\implies \mathtt{(x-2) = 0 \;\;\;\; or \;\;\;\; (2x-3) = 0}$

$\implies \mathtt{x = 2 \;\;\;\; or \;\;\;\; x = \large\frac{3}{2}}$

$\texttt{Hence, \; the \; roots \; of \; the \; polynomial} \\ \mathtt{2x²-7x+6} \; \texttt{is \; x} \; \mathtt {= 2}\;\; \& \;\; \texttt{x} \; \mathtt{= \large \frac{3}{2}}.$