Question

what is the roots of quadratic equation root2x²+9=0​

Answer 1

Answer:

$\huge\boxed{x=\pm\dfrac{3i\sqrt2}{2}}\\\boxed{\bold{NO\ REAL\ ROOTS}}$

Step-by-step explanation:

$2x^2+9=0\qquad|\text{subtract 9 from both sides}\\\\2x^2=-9\qquad|\text{divide both sides by 2}\\\\x^2=-\dfrac{9}{2}<0\\\\\bold{NO\ REAL\ ROOTS}\\\\\text{In the complex set:}\\\\x^2=-\dfrac{9}{2}\to x=\pm\sqrt{-\dfrac{9}{2}}\\\\x=\pm\dfrac{\sqrt{-9}}{\sqrt2}\\\\x=\pm\dfrac{3i}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\x=\pm\dfrac{3i\sqrt2}{2}$