The Roots of the Quadratic Equation √3x²- 2√2x – 2√3 = 0 are

By BYJU'S Exam Prep

Updated on: October 17th, 2023

The roots of the quadratic equation √3x²- 2√2x – 2√3 = 0 are

Here the important steps which will be used to find the solution of given quadratic equation.

Step 1: Identify the coefficients of the quadratic equation. In this case, the coefficients are
Step 2: Use the quadratic formula to find the roots
Step 3: Use rationalisation of denominator to get the roots.

Table of content

Solution:

Given Equation:

√3x² – 2√2x – 2√3 = 0

Simplified Equation:

x² – 2√6x – 2√3 = 0

Finding the Roots:

To find the roots of the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² – 4ac)) / (2a)

In this case, the coefficients are:

a = √3

b = -2√2

c = -2√3

Plugging in the values into the quadratic formula, we have:

x = (-(-2√2) ± √((-2√2)² – 4(√3)(-2√3))) / (2(√3))

Simplifying further:

x = (2√2 ± √[(4)(2) + (8)(3)]) / 2√3

x = (2√2 ± √(8 + 24)) / 2√3

x = (2√2 ± 4√2) / 2√3

Now the two roots will be:

x = (2√2 + 4√2) / 2√3 and x = (2√2 – 4√2) / 2√3

x = 3√2/√3 and x = -√2/√3

Now, rationalising the denominator:

x = [3√2(√3)]/√3(√3) and x = [-√2(√3)]/√3(√3)

x = √6 and -√6/3

Finally, we have the roots:

x₁= √6

x₂ = -√6/3

Answer:

Roots of the Quadratic Equation √3x²- 2√2x – 2√3 = 0 are x =√6 and x = -√6/3

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