Find the roots of the following quadratic equ | vedclass

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

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$x = 1, x = 2/3$

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(A) The given quadratic equation is $3x^{2} - 5x + 2 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 3$,$b = -5$,and $c = 2$.First,calculate the discriminant $D = b^{2} - 4ac$:$D = (-5)^{2} - 4(3)(2) = 25 - 24 = 1$.Since $D > 0$,real and distinct roots exist.Using the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$:$x = \frac{-(-5) \pm \sqrt{1}}{2(3)} = \frac{5 \pm 1}{6}$.Case $1$: $x = \frac{5 + 1}{6} = \frac{6}{6} = 1$.Case $2$: $x = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3}$.Thus,the roots are $1$ and $\frac{2}{3}$.

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $3x^{2} - 5x + 2 = 0$.

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