Question

For a quadratic equation of the form $a{x}^2+bx+c=0;a,b,c\in R,a\ne 0,$ which of the given statements is/are true?

• A. $D<0$, the roots are imaginary
• B. $D=0$, the roots are real and equal
• C. $D>0$, the roots are real and distinct
• D. $D<0,$ the roots are real and distinct

Answer 1

Answer: (A), (B), (C)

$D>0$, the roots are real and distinct

For a quadratic equation of the form $a{x}^2+bx+c=0;a,b,c\in R,a\ne 0$
The Discriminant is given as $D=b^2-4ac.$
The three possible cases for the discriminant are:
$a.D>0$
In this case the roots are real but distinct.
$b.D<0$
In this case the roots are imaginary.
$c.D=0$
In this case the roots are real and equal.