Question

Determine the nature of the roots of the equation. 3x^2 - 2 * root6 x +2=0

Answer 1

AnswEr :

Given Equation,

3x² - 2√6x + 2 = 0

Comparing the above equation with ax² + bx + c = 0,

• a = 3
• b = - 2√6
• c = 2

We have to determine the nature of the roots of the above equation

NoTE

Let D be the discriminant of the equation ax² + bx + c = 0

D = b² - 4ac

• If D > 0,the roots are real and distinct

• If D = 0,the roots are real and equal

• If D < 0,the roots are imaginary

(Putting the values)

D = (-2√6)² - 4(3)(2)

» D = 24 - 24

» D = 0_____________Thus,the roots are real and equal

Answer 2

Given: 3x² - 2√6x + 2 = 0.

To find: The nature of its roots.

Answer:

Let's suppose ax² + bx + c = 0 is a quadratic equation.

Then, it's discriminant would be given by b² - 4ac.

CONDITIONS TO DETERMINE THE NATURE OF THE ROOTS:

• If b² - 4ac = 0, the roots are real and equal.
• If b² - 4ac < 0, the roots are unreal.
• If b² - 4ac > 0, the roots are real and distinct.

From the given equation, we have:

• a = 3
• b = -2√6
• c = 2

Using the discriminant equation,

(-2√6)² - 4(3)(2)

= (4*6) - 24

= 24 - 24

= 0

Since b² - 4ac = 0, the roots are real and equal.