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Question

(A) Given the quadratic equation: $3x^2 + 5\sqrt{2}x - 2 = 0$.Comparing this with the standard form $ax^2 + bx + c = 0$,we get $a = 3$,$b = 5\sqrt{2}$

Vedclass · Accepted Answer

$\frac{-5\sqrt{2} + \sqrt{74}}{6}, \frac{-5\sqrt{2} - \sqrt{74}}{6}$

Vedclass · Answer

(A) Given the quadratic equation: $3x^2 + 5\sqrt{2}x - 2 = 0$.Comparing this with the standard form $ax^2 + bx + c = 0$,we get $a = 3$,$b = 5\sqrt{2}$,and $c = -2$.The discriminant $D$ is given by $D = b^2 - 4ac$.$D = (5\sqrt{2})^2 - 4(3)(-2) = (25 	imes 2) + 24 = 50 + 24 = 74$.Since $D > 0$,the equation has two distinct real roots.The quadratic formula is $x = \frac{-b \pm \sqrt{D}}{2a}$.Substituting the values: $x = \frac{-5\sqrt{2} \pm \sqrt{74}}{2(3)} = \frac{-5\sqrt{2} \pm \sqrt{74}}{6}$.Thus,the solutions are $x = \frac{-5\sqrt{2} + \sqrt{74}}{6}$ and $x = \frac{-5\sqrt{2} - \sqrt{74}}{6}$.

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $3x^2 + 5\sqrt{2}x - 2 = 0$.

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