Answer:

The nature of quadratic equation is no real roots.

Step-by-step explanation:

Given : Quadratic equation 2x²=a–4x

To find : Nature of the roots of quadratic equation?

Solution :

To determine the nature we find discriminant, D=b2−4ac

1) If D<0, no real roots.

2) If D=0, two equal real roots.

3) If D>0, two distinct real roots.

Now, we find discriminant.

2x²–4x+a=0

Here, a=2,b=-4,c=a(1)

D=(-4)²–4(2) (a)

D= 16–8a

D= 8a

So, D<0 there is no real roots.

Therefore, The nature of quadratic equation is no real roots.