Question

Find the roots of the following quadratic (if they exist) by the method of completing the square.
√3x²+10x+7√3=0

Answer 1

$\text{Given equation is}$

$\sqrt{3}x^2+10x+7\sqrt{3}=0$

$\text{To make the coefficient of x^2 , divide by \sqrt{3} }$

$x^2+\frac{10}{\sqrt{3}}x+7=0$

$x^2+\frac{10}{\sqrt{3}}x=-7$

$\text{To make the L.H.S as a perfect square,}$$\;\text{add \frac{25}{3} on both sides}$

$x^2+\frac{10}{\sqrt{3}}x+\frac{25}{3}=\frac{25}{3}-7$

$(x+\frac{5}{\sqrt{3}})^2=\frac{25-21}{3}$

$(x+\frac{5}{\sqrt{3}})^2=\frac{4}{3}$

$\text{Taking square root on bothsides, we get}$

$x+\frac{5}{\sqrt{3}}=\pm\frac{2}{\sqrt{3}}$

$x=\frac{-5}{\sqrt{3}}\pm\frac{2}{\sqrt{3}}$

$x=\frac{-5+2}{\sqrt{3}},\;\frac{-5-2}{\sqrt{3}}$

$x=\frac{-3}{\sqrt{3}},\;\frac{-7}{\sqrt{3}}$

$x=-\sqrt{3},\;\frac{-7}{\sqrt{3}}$

$\therefore\textbf{The solution set is}\;\{\bf\,-\sqrt{3},\;\frac{-7}{\sqrt{3}}\}$

Find more:

Find the roots of the following quadratic (if they exist) by the method of completing the square.

2x²-7x+3=0

https://brainly.in/question/15926789

Answer 2

Given:-

• √3x² +10x +7√3 = 0

To find:-

• Find the roots of the equation..?

Solutions:-

• √3x² +10x +7√3 = 0

Now divide throughout by √3. we get.

=> x² + 10x/√3 + 7 = 0

Now take the constant term to the RHS and we get

=> x² + 10x/√3 = -7

Now add square of half of co - efficient of x on both the sides . we have,

=> x² + 10x/√3 + (10/2√3)² = (10/2√3)² - 7

=> x² + (10/2√3)² + 2(10/2√3)x = 16/12

=> (x + 10/2√3)² = 16/12

Since RHS is a positive integer, therefore the roots of the equation exist.

So, now take the square root on both the sides and we get.

=> x + 10/2√3 = +,- 4/2√3

=> x = -10/2√3 +,- 4/2√3

Now, we have the value of x

=> x = -10/2√3 + 4/2√3

=> x = -√3

Also we have,

=> x = -10/2√3 - 4/2√3

=> x = 7/√3

Hence, the roots of the equation are -√3 and -7/√3