Question

Find the nature of Roots. :2x square-underroot5x + 1=0

Answer 1

Given :

Equation is : 2 x² - √5 x + 1 = 0

Comparing with a x² +  b x + c

a = 2

b = -√5

c = 1

Discriminant Δ = b² - 4 ac

b² - 4 ac

==> (-√5)² - 4.1.2

==> 5 - 8

==> - 3

Since b² - 4 ac < 0

roots are not real

The equation does not have real roots !

Hope it helps u :-)

___________________________________________________________________

Answer 2

Answer:

Imaginary Roots

Step-by-step explanation:

Concept: To determine nature of roots there are 3 cases.

Case 1: When the discriminant is greater than 0, then the equation has real roots.

Case 2: When discriminant is equal to 0, then the equation has equal roots.

Case 3: When the discriminant is less than 0, then the equation has imaginary roots.

According to this question, the given equation is: 2x² - √5 x + 1 =0

Discriminant = b² - 4ac

Here,

• a = 2
• b = - √5
• c = 1

Applying in the discriminant we get,

⇒ ( -√5 )² - 4 ( 2 ) ( 1 )

⇒ 5 - 8 = -3

We know that, -3 < 0.

So the equation will fall in Case 3 which means, it has imaginary roots.

Hope my answer helped !!