Question

Find roots
$\sf \sqrt{2}x^{2} +7x+5\sqrt{2}$

Answer 1

Need-to-know

Roots

The roots are numbers that satisfy the equation.

Quadratic Equation

It is an equation with the highest degree of 2. There are three ways to solve this equation.

-Factorization

For a number to be zero, its factor needs to be zero.

-Complete the Square

This uses the concept of the square root. After we learn this, we learn how to derive the formula.

-Quadratic Formula

This is a general method of solving this equation if factorization doesn't work.

Solution

Sol. Factorization

Let us equate zero, to solve the equation.

$\sqrt{2} x^2+7x+5\sqrt{2} =0$

Let us multiply equal number, $\sqrt{2}$ on both sides. This keeps the equality of the equation.

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

Now let's start the factorization.

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

$\sqrt{2} x$                    $5$

$\sqrt{2} x$                    $2$

Let us apply this,

$x^2+(a+b)x+ab=(x+a)(x+b)$

$\therefore (\sqrt{2} x+5)(\sqrt{2} x+2)=0$

The factor needs to be zero.

Then, our desired solutions are $\boxed{x=-\dfrac{5\sqrt{2}}{2} }$ or$\boxed{x=-\sqrt{2}}$.

Answer 2

Question

Find roots $\sf \sqrt{2}x^{2} +7x+5\sqrt{2}$

To Find:-

• Find the roots.

Solution:-

Here ,

We have to factor $\sf \sqrt{2}x^{2} + 7x + 5\sqrt{2} = 0$

$\sf\implies \sqrt{2}x^{2} + 2x + 5x + 5\sqrt{2} = 0$

$\sf\implies x\sqrt{ 2 } ( x + \sqrt { 2 } ) + 5( x + \sqrt { 2 } ) = 0$

$\sf\implies ( x\sqrt { 2 } + 5 ) ( x + \sqrt { 2 } ) = 0$

$\sf\implies x = \dfrac { - 5 } { \sqrt { 2 } } , - \sqrt { 2 }$

Hence ,

• Roots are $\sf \dfrac { - 5 } { \sqrt { 2 } } , - \sqrt { 2 }$