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

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 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`

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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
Chapter 4 Quadratic Equations
Exercise 4.6 | Q 1.4 | Page 41
NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.4 | Q 1.2 | Page 91
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