Solve the equation 3x^{2} - 4x + frac{20}{3} | vedclass

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(A) The given quadratic equation is $3x^{2} - 4x + \frac{20}{3} = 0$.Multiplying the entire equation by $3$,we get $9x^{2} - 12x + 20 = 0$.Comparing t

Vedclass · Accepted Answer

$\frac{2}{3} \pm \frac{4}{3}i$

Vedclass · Answer

(A) The given quadratic equation is $3x^{2} - 4x + \frac{20}{3} = 0$.Multiplying the entire equation by $3$,we get $9x^{2} - 12x + 20 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we have $a = 9$,$b = -12$,and $c = 20$.The discriminant $D$ is given by $D = b^{2} - 4ac = (-12)^{2} - 4(9)(20) = 144 - 720 = -576$.Using the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$,we get:$x = \frac{-(-12) \pm \sqrt{-576}}{2(9)} = \frac{12 \pm \sqrt{576}i}{18} = \frac{12 \pm 24i}{18}$.Simplifying the expression,we get $x = \frac{12}{18} \pm \frac{24}{18}i = \frac{2}{3} \pm \frac{4}{3}i$.

Solve the equation $3x^{2} - 4x + \frac{20}{3} = 0$.

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