Question

For the quadratic equation $a{x}^2+bx-4=0,a,b\in R$ and $a>0,$ then which of the following is always 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

$a{x}^2+bx-4=0,a,b\in R$ and $a>0$

$D=b^2+16a>0(\because a>0)$
Real and distinct roots
Product of roots
$=-\frac{4}{a}<0$
Roots are opposite in sign.

Hence, the roots are real, distinct and have opposite sign.