Question

Solutions of the quadratic equation √3x 2 -2√2x - 2√3 = 0, are a) √3 and √6 b) -2√3 and - √6 c) - √6/3 and √6 d) 2√3 and √6

Answer 1

$\huge\bf{★Answer:-}$

Given:-

• The quadratic equation is $\sf{\sqrt{3}x^2 -2 \sqrt{2}x -2\sqrt{3}= 0}$

To Find:-

• Solution of the equation.

Solution:-

⇒$\sf{\sqrt{3}x^2 -2 \sqrt{2}x -2\sqrt{3}= 0}$

Now , by doing Middle term , we get

⇒$\sf{\sqrt{3}x^2 - (3 -1 )\sqrt{2}x -2\sqrt{3}= 0}$

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

⇒$\sf{\sqrt{3}x (x- \sqrt{6}) + \sqrt{2}(x - \sqrt{6}}=0$

⇒$\sf{(x - \sqrt{6}) ( \sqrt{3}x + \sqrt{2})= 0}$

Either ,

↦$\sf{(x - \sqrt{6})= 0}$

$\therefore{x}$ = $\sf{\sqrt{6}}$

Or,

↦$\sf{( \sqrt{3}x + \sqrt{2})= 0}$

↦$\sf{ \sqrt{3}x = - \sqrt{2}}$

$\therefore{x}$$\sf{= -\sqrt{2}/ \sqrt{3}}$

so, x = √6 and -√2/√3

★ Things to Know:-

• A Quadratic equation is usually expressed in the form of ax² + bx + c = 0 . It is its Standard form . [ where a ≠ 0 ]

• If a becomes zero then it will be Linear equation .

• The graph of a quadratic equation is parabola.

• The degree of x in quadratic equation is 2 .

• In Quadratic Equation there two root exist .

★ Solution to find Roots of Quadratic Equation:-

We can find the roots of any quadratic equation by the following methords :-

• By Doing Middle term Factor.

• By using Quadratic Formulla .

• By Compleating Square .