The given quadratic equations have real roots and the roots are $-\sqrt2, \, \dfrac{-5}{\sqrt2}$ : $\sqrt{2}x^2 \, + \, 7x \, + \, 5\sqrt{2} \, = \, 0$

To factorize the quadratic expression the square root of 2 times x squared plus 7x plus 5 times the square root of 2, we use the method of splitting the middle term. The product of the first and last terms is 10, so we split the middle term into 2x and 5x. This gives the square root of 2 times x squared plus 2x plus 5x plus 5 times the square root of 2, which factors into x multiplied by (the square root of 2 times x plus 2) plus the square root of 2 multiplied by (the square root of 2 times x plus 2). Setting the factors (x plus the square root of 2) and (the square root of 2 times x plus 5) to zero gives the roots as negative the square root of 2 and negative 5 divided by the square root of 2. Therefore, the statement is True.

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