Question

determine the nature of roots (b + c)x2 - (a + b + c) x + a = 0​

Answer 1

Step-by-step explanation:

$Given \: it \\ {(b + c)} {x}^{2} - (a + b)x + a = 0 \\ \\ To \: determine \: nature \: of \: roots \:, \: we \: \\ find \: out \: \: \: \: D = {B}^{2} - 4AC \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ( {a + b)}^{2} - 4a(b + c) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {a}^{2} + {b}^{2} + 2ab - 4ab - 4ac \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {a}^{2} + {b}^{2} - 2ab - 4ac \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ( {a - b)}^{2} - 4ac \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = D > 0 \\ \\ Hence \: roots \: are \: rational \:, distinct. \\ \\ Hope \: it \: wil \: help \: you..$