Question

Solve :x^2+2 root 3x +3=0

Answer 1

Concept:

Roots are the factors or solutions of the expression either in the form of number or expression.

Given:

x² + 2√(3x) + 3 = 0

Find:

We are asked to solve  x² + 2√(3x) + 3 = 0.

Solution:

We have,

x² + 2√(3x) + 3 = 0

Now,

Using the mid-term splitting method,

i.e.

The product of the coefficient of  x² and the Constant term should give the middle term when added or subtracted,

So,

x² + 2√(3x) + 3 = 0

Now,

x² + √(3x) + √(3x) + 3 = 0

Now,

Taking common,

i.e.

x(x + √3 ) + √3(x + √3 ) = 0

Now,

Again taking common,

We get,

(x + √3 ) (x + √3 ) = 0

Now,

(x + √3 ) = 0

We get,

x = -√3

Now,

(x + √3 ) = 0

We get,

x = -√3

Hence, the roots of the given expression are -√3 and -√3.

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Answer 2

Answer:

The roots of the equation $x^2+2\sqrt{3}\ x+3=0$ are $-\sqrt{3}$ and $-\sqrt{3}$.

Step-by-step explanation:

Step 1 of 2

Consider the quadratic equation as follows:

$x^2+2\sqrt{3}\ x+3=0$

Using the middle-term splitting method,

We need to find the two numbers $a$ and $b$ such that $a+b=2\sqrt{3}$ and $ab=3$.

Notice that the numbers $\sqrt{3}$ and $\sqrt{3}$ gives the sum as $2\sqrt{3}$ and the product as $3$.

(Since $\sqrt{3}\times \sqrt{3}=3$)

Step 2 of 2

Finding the roots of the equation.

Factorising the given equation as follows:

⇒ $x^2+\sqrt{3}\ x+\sqrt{3}\ x+3=0$

⇒ $x(x+\sqrt{3})+\sqrt{3}(x+\sqrt{3})=0$

Taking the term $(x+\sqrt{3})$ common out, we get

⇒ $(x+\sqrt{3})(x+\sqrt{3})=0$

⇒ $x=-\sqrt{3}$ and $x=-\sqrt{3}$

Therefore, the roots of the equation $x^2+2\sqrt{3}\ x+3=0$ are $-\sqrt{3}$ and $-\sqrt{3}$.

The roots of the given equation are repeated roots.

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