Question

If $aandb$ are the roots of the equation $x^2+ax+b=0,a\ne 0,b\ne 0,$ the values of $aandb$ are respectively

• A. $2and-2$
• B. $2and-1$
• C. $1and–2$
• D. $1and2$
• E. – 1 and 2

Answer 1

The correct option is C

$1and–2$

The explanation for the correct option:

The given equation is $x^2+ax+b=0,a\ne 0,b\ne 0,$

Since

$\begin{array}{rcl}Sumoftheroots& =& a+b\\ & =& –a\\ Productoftheroots& =& ab\\ & =& b\end{array}$

Hence,

$\begin{array}{rcl}2a+b& =& 0;ab–b=0\\ 2a& =& –b;(a–1)b=0\\ 2a& =& –b;a=1\\ sinceb& \ne & 0\\ b& =& –2\\ a& =& 1\end{array}$

Hence, the correct answer is option (C).