Question

What is the nature of the roots of the quadratic equation 2x²-3x-4=0​

Answer 1

Answer:

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Answer 2

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

+3x−4=0 is in the form ax

2

+bx+c=0 where a=1,b=3 and c=−4, therefore,

b

2

−4ac=(3)

2

−(4×1×−4)=9+16=25>0

Since b

2

−4ac>0

Hence the roots are real and distinct.