The roots of the quadratic equation $\displaystyle \sqrt 2 x^2 + 7x + 5\sqrt 2 = 0$ are
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The two roots are $\displaystyle \frac{3}{\sqrt{2}} $ and $ -\dfrac{6}{\sqrt 5}$
- The two roots are $\displaystyle \sqrt 7 $ and $ -\dfrac{5}{\sqrt 2}$
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The two roots are $\displaystyle -\frac{7}{\sqrt{2}} $ and $ -\dfrac{6}{\sqrt 5}$
- The two roots are $\displaystyle -\sqrt 2 $ and $ -\dfrac{5}{\sqrt 2}$
Solve sqrt(2)x^2 + 7x + 5*sqrt(2) = 0. Using the quadratic formula or factoring: sqrt(2)x^2 + 2x + 5x + 5*sqrt(2) = 0. sqrt(2)x(x + sqrt(2)) + 5(x + sqrt(2)) = 0. (sqrt(2)x + 5)(x + sqrt(2)) = 0. Roots are -sqrt(2) and -5/sqrt(2).
Using the splitting the middle term method for the quadratic equation root 2 x squared + 7x + 5 root 2 equals 0, we find the product of the coefficients of x squared and the constant term is 10. We split the middle term 7x into 5x + 2x to get root 2 x squared + 5x + 2x + 5 root 2 equals 0. Factoring by grouping gives x(root 2 x + 5) + root 2(root 2 x + 5) equals 0, which results in (x + root 2)(root 2 x + 5) equals 0. Equating each part to zero gives x equals negative root 2 and x equals negative 5 divided by root 2. The roots are negative root 2 and negative 5 divided by root 2.