Solve 10z^2+4z+9 - ScanMath

Question

Find the roots

z_{1} = - \frac{1}{5} - \frac{86}{10} i, z_{2} = - \frac{1}{5} + \frac{86}{10} i

Alternative Form

z_{1} \approx - 0.2 - 0.927362 i, z_{2} \approx - 0.2 + 0.927362 i

Evaluate

10 z^{2} + 4 z + 9

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

10 z^{2} + 4 z + 9 = 0

Substitute a= 10,b= 4 and c= 9 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{- 4 \pm 4 ^{2} - 4 \times 10 \times 9}{2 \times 10}

Simplify the expression

z = \frac{- 4 \pm 4 ^{2} - 4 \times 10 \times 9}{20}

Simplify the expression

More Steps

z = \frac{- 4 \pm - 344}{20}

Simplify the radical expression

More Steps

z = \frac{- 4 \pm 2 86 \times i}{20}

Separate the equation into 2 possible cases

z = \frac{- 4 + 2 86 \times i}{20} z = \frac{- 4 - 2 86 \times i}{20}

Simplify the expression

More Steps

z = - \frac{1}{5} + \frac{86}{10} i z = \frac{- 4 - 2 86 \times i}{20}

Simplify the expression

More Steps

z = - \frac{1}{5} + \frac{86}{10} i z = - \frac{1}{5} - \frac{86}{10} i

Solution

z_{1} = - \frac{1}{5} - \frac{86}{10} i, z_{2} = - \frac{1}{5} + \frac{86}{10} i

Alternative Form

z_{1} \approx - 0.2 - 0.927362 i, z_{2} \approx - 0.2 + 0.927362 i

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