Question

The quadratic equation $a{x}^2+bx+c=0$ will always have imaginary roots if:

• A. $a<-1,0<c<1,b<0$
• B. $a<-1,-1<c<0,0<b<1$
• C. $a<-1,c<0,b>1$
• D. $a<-1,c<-1,1<b<2$

Answer 1

Answer: (D)

$a<-1,c<-1,1<b<2$

The quadratic equation $a{x}^2+bx+c=0$ will have imaginary roots if discriminant is negative

So, $D$ must be negative,

$\Rightarrow b^2-4ac<0$

$\Rightarrow b^2<4ac$

Now we need to examine each option, only D will satisfy.