Question

2. Nature of roots of the equation x2 + 2x + 4=0​

Answer 1

Answer:

We know that while finding the root of a quadratic equation ax

2

+bx+c=0 by quadratic formula x=

2a

−b±

b

2

−4ac

,

if b

2

−4ac>0, then the roots are real and distinct

if b

2

−4ac=0, then the roots are real and equal and

if b

2

−4ac<0, then the roots are imaginary.

Here, the given quadratic equation x

2

−2x+3=0 is in the form ax

2

+bx+c=0 where a=1,b=−2 and c=3, therefore,

b

2

−4ac=(−2)

2

−(4×1×3)=4−12=−8<0

Since b

2

−4ac<0

Hence the roots are imaginary or no real roots.