find the zeros
\[
3 x^{2}-2 x-8=0
\]

Answer

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Answer

\boxed{x_1 = 2.0, x_2 = -\frac{4}{3}}

Steps

Step 1 ：Given the quadratic equation \(3x^2 - 2x - 8 = 0\), we can find the zeros using the quadratic formula: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Step 2 ：Substitute the coefficients a = 3, b = -2, and c = -8 into the formula: \[x = \frac{2 \pm \sqrt{(-2)^2 - 4(3)(-8)}}{2(3)}\]

Step 3 ：Calculate the discriminant and simplify the expression: \[x = \frac{2 \pm \sqrt{100}}{6}\]

Step 4 ：Find the two zeros: \[x_1 = \frac{2 + 10}{6} = 2.0\] and \[x_2 = \frac{2 - 10}{6} = -\frac{4}{3}\]

Step 5 ：\boxed{x_1 = 2.0, x_2 = -\frac{4}{3}}

find the zeros\[3 x^{2}-2 x-8=0\]

Answer

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find the zeros
\[
3 x^{2}-2 x-8=0
\]