Question

If the roots of the quadratic equation $x^2+(a+6)x+b=0$ are real and distinct for all $a\in R$ then the range of values of b is

• A. $(-\infty ,\infty )$
• B. $(-\infty ,0)$
• C. $(-6,\infty )$
• D. none of these

Answer 1

The correct option is B $(-\infty ,0)$

$D>0\Rightarrow (a+6{)}^2-4b>0forallreal{}^{\prime }{a}^{\prime }\Rightarrow b<0$.