Problem

find the zeros of \( 3 x^{2}+13 x-10=0 \)

Answer

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Answer

\( x_2 = -5 \)

Steps

Step 1 :\( \Delta = b^{2} - 4 a c \)

Step 2 :\( \Delta = 13^{2} - 4 \times 3 \times (-10) \)

Step 3 :\( \Delta = 169 + 120 \)

Step 4 :\( \Delta = 289 \)

Step 5 :\( x_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2a} \)

Step 6 :\( x_{1,2} = \frac{-13 \pm \sqrt{289}}{2 \times 3} \)

Step 7 :\( x_1 = \frac{-13 + 17}{6} \)

Step 8 :\( x_1 = \frac{4}{6} \)

Step 9 :\( x_1 = \frac{2}{3} \)

Step 10 :\( x_2 = \frac{-13 - 17}{6} \)

Step 11 :\( x_2 = \frac{-30}{6} \)

Step 12 :\( x_2 = -5 \)

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