# Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; 3x^2 - 4sqrt3x + 4 = 0 - Mathematics

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;

3x^2 - 4sqrt3x + 4 = 0

Determine the nature of the roots of the following quadratic equation:

3x^2 - 4sqrt3x + 4 = 0

#### Solution

3x^2 - 4sqrt3x + 4 = 0

Comparing it with ax2 + bx + c = 0, we get

a = 3, b = -4sqrt3  and c = 4

Discriminant = b2 - 4ac

= (-4sqrt3)^2 - 4(3)(4)

= 48 - 48 = 0

As b2 - 4ac = 0,

Therefore, real roots exist for the given equation and they are equal to each other.

And the roots will be (-b)/(2a)

Therefore, the roots are 2/sqrt3 and 2/sqrt3.

Concept: Nature of Roots
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#### APPEARS IN

RD Sharma Class 10 Maths
Exercise 4.6 | Q 1.4 | Page 41
NCERT Class 10 Maths