Question

Find the roots of the following quadratic equation
by factorisation method.
√2x² + 7x+5√2=0
​

Answer 1

Answer:

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

Step-by-step explanation:

To find the roots of the given equation by factorization method .

follow the steps given below.

Given:-

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

1)now you should have to multiply the last term and first term.

$= > 5 \sqrt{2} \times \sqrt{2} {x}^{2} = 5 \times 2 {x}^{2} \\ = 10 {x}^{2}$

2) take the two numbers , from which by multiply or divide them we get 10x^2 and by adding or subtraction we get the middle term that is 7x.

3) let the two numbers are 5x and 2x

because, by multiply 5x and 2x we get 10x square. also by adding 5x and 2x we get 7x .

4) split the middle term as shown below:-

$= > \sqrt{2} {x}^{2} + 5x + 2x + 5 \sqrt{2} = 0 \\ take \: common \: x \: and \: \sqrt{2} \\ = > x(\sqrt{2} x + 5) + \sqrt{2} ( \sqrt{2}x + 5) \\ = > (x + \sqrt{2}) ( \sqrt{2} + 5)$

hence the roots are ,

$x + \sqrt{2} = 0 \: \: \: \: or \: \: \: \sqrt{2} x + 5 = 0 \\ x = - \sqrt{2} \: \: \: \: or \: \: x = - \frac{5}{ \sqrt{2} }$

Hope it helps you.

mark it brainliest ☺️.