Question

find whether the roots of the equation is rational ????????
(a+(-b))x2 + 2cx +(b+c-a)=0

Answer 1

Answer:

Not sure about the answer

Answer 2

$\huge \sf {Question :-}$

find whether the roots of the equation is rational ????????

(a+(-b))x2 + 2cx +(b+c-a)=0

$\huge \sf{Answer :-}$

$\huge\mathrm{\underline{Given:}}$

$\tt{Equation:-}(a + ( - b)) {x}^{2} + 2cx + (b + c - a) = 0 \\ \\ \tt{where:} \: \\ a = (a + ( - b)) \\ b = 2c \\ c = (b + c - a)$

$\huge\mathrm{\underline{solution:-}}$

$\tt{D = {b}^{2} - 4ac } \\ = \tt{4 {c}^{2} - 4(a + ( - b)(b + c - a)} \\ \\ = 4( {c}^{2} - (ab + \cancel{ac} - {a}^{2} + \cancel{bc} + {c}^{2} - \cancel{ac} - {b}^{2} - \cancel{bc} + ab) \\ = 4( {c}^{2} - (2ab - {a}^{2} + {c}^{2} - {b}^{2} )) \\ = 4( {c}^{2} - 2ab + {a}^{2} - {c}^{2} + {b}^{2} ) \\ \\ = 4 {(a - b)}^{2} \\ \\ \tt\green{\underline{\underline{hence \: the \: roots \: are \: rational}}}$