Solve 3y^(2)-8y+9

Question

Find the roots

Find the roots of the algebra expression

y_{1} = \frac{4}{3} - \frac{11}{3} i, y_{2} = \frac{4}{3} + \frac{11}{3} i

Alternative Form

y_{1} \approx 1. \dot{3} - 1.105542 i, y_{2} \approx 1. \dot{3} + 1.105542 i

Evaluate

3 y^{2} - 8 y + 9

To find the roots of the expression,set the expression equal to 0

3 y^{2} - 8 y + 9 = 0

Substitute a= 3,b= - 8 and c= 9 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 \times 9}{2 \times 3}

Simplify the expression

y = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 \times 9}{6}

Simplify the expression

More Steps

y = \frac{8 \pm - 44}{6}

Simplify the radical expression

More Steps

y = \frac{8 \pm 2 11 \times i}{6}

Separate the equation into 2 possible cases

y = \frac{8 + 2 11 \times i}{6} y = \frac{8 - 2 11 \times i}{6}

Simplify the expression

More Steps

y = \frac{4}{3} + \frac{11}{3} i y = \frac{8 - 2 11 \times i}{6}

Simplify the expression

More Steps

y = \frac{4}{3} + \frac{11}{3} i y = \frac{4}{3} - \frac{11}{3} i

Solution

y_{1} = \frac{4}{3} - \frac{11}{3} i, y_{2} = \frac{4}{3} + \frac{11}{3} i

Alternative Form

y_{1} \approx 1. \dot{3} - 1.105542 i, y_{2} \approx 1. \dot{3} + 1.105542 i

Show Solution