Question

For $a,b,c\in Q$ and $b+c\ne a$, the roots of $a{x}^2-(a+b+c)x+(b+c)=0$ are

• A. Rational and unequal
• B. rational and equal
• C. complex numbers
• D. none

Answer 1

The correct option is A Rational and unequal

$a{x}^2-(a+b+c)x+(b+c)=0$

$D=(a+b+c{)}^2-4a(b+c)$

$=a^2+b^2+c^2+2ab+2bc+2ac-4ab-4ac$

$=a^2+b^2+c^2-2ab-2ac+2bc$

$=(a-b-c{)}^2$

=perfect sqaure

$\therefore$ rational and unequal roots