Question

For the quadratic equation $a{x}^2+bx+c=0,a,b,c\in R$ and $ac<0,$ then which of the following is true ?

• A. roots are real, distinct and have same sign
• B. roots are real, distinct and have opposite sign
• C. roots are not real
• D. roots are real and repeated

Answer 1

The correct option is B roots are real, distinct and have opposite sign

$a{x}^2+bx+c=0,a,b,c\in R$
$\Delta =b^2-4ac>0(\because ac<0)$
$\therefore$ Roots are real and distinct.
Also, $ac<0\Rightarrow \frac{c}{a}<0$
$\therefore$ Roots will have opposite sign.
Hence, roots are real, distinct and have opposite sign.