Question

Find the factorization method of X^2+2√2x+2=0

Answer 1

CorreCt Que:-

Find the roots of $\sf x^2+2\sqrt{2}x+2=0$ by factorization method

AnswEr:-

Given equation:-

$\tt\longrightarrow x^2+2\sqrt{2}x+2=0$

To Find:-

The zeroes of given equation by factorization method.

Now here,

$\tt\longrightarrow Coefficient of x^2\times constant term = 2. \\ \\ \tt Also\\ \\ \tt\longrightarrow 2 = \sqrt{2}\times\sqrt{2}. \\ \\ \tt And, \\ \\ \tt\longrightarrow \sqrt{2}+\sqrt{2} = 2\sqrt{2} = Middle\:\: Term.$

So lets factorize the equation by splitting middle term:-

$\tt\mapsto {x}^{2} + 2 \sqrt{2} x + 2 = 0. \\ \\ \tt\mapsto {x}^{2} + ( \sqrt{2} + \sqrt{2})x + 2 = 0. \\ \\ \tt\mapsto {x}^{2} + \sqrt{2} x + \sqrt{2} x + 2 = 0. \\ \\ \tt\mapsto x(x + \sqrt{2} ) + \sqrt{2} (x + \sqrt{2}) = 0. \\ \\ \tt\mapsto(x + \sqrt{2} ) {}^{2} = 0 \\ \\ \tt\mapsto x + \sqrt{2} = \sqrt{0} . \\ \\ \tt\mapsto x + \sqrt{2} = 0 \\ \\ \tt\mapsto x = - \sqrt{2} \\ \\ \tt \: \: which \: \: is \: \: no t \: \: possible.$

As every square root must have a positive value but here it is negative.

$\therefore$ The given equation does not have any real roots.