Question

10m^2 - 11m + 4 = 0step by step

Answer 1

EXPLANATION

Given the equation 10m^2 - 11m + 4 = 0

We can see that this is a quadratic equation so we need to apply the quadratic formula as shown as follows:

`m_(1,2)=\frac{-(-11)\pm\sqrt[]{(-11)^2-4\cdot10\cdot4}}{2\cdot10}`

Simplifying:

`m_(1,2)=\frac{11\pm\sqrt[]{121-160}}{20}`
`m_(1,2)=\frac{11\pm\sqrt[]{-39}}{20}`

Separate the solutions:

`m_1=\frac{11+\sqrt[]{39}i}{20}`
`m_2=\frac{11-\sqrt[]{39}i}{20}`

Rewritting the expressions:

`m_1=(11)/(20)+\frac{\sqrt[]{39}i}{20}`
`m_2=(11)/(20)-\frac{\sqrt[]{39}i}{20}`

The solutions to the quadratic equations are:

`m_{}=(11)/(20)+i\frac{\sqrt[]{39}}{20}`
`m=(11)/(20)-i\frac{\sqrt[]{39}}{20}`