Question

I need help with figuring out the value and the answer to m

Answer 1

Given the quadratic equation below

`3m^2+m-5=0`

To find m in the form

`m=\frac{N\pm\sqrt[]{D}}{M}`

Using the quadratic formula

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where x}=m \\ m=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

The general form of a quadratic equation is

`ax^2+bx+c=0`
`\begin{gathered} \text{Where } \\ a=3,b=1,c=-5 \end{gathered}`

Substitute for a, b and c into the quadratic formula above

`\begin{gathered} m=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ m=\frac{-1\pm\sqrt[]{(1)^2-4(3)(-5)}}{2(3)} \\ m=\frac{-1\pm\sqrt[]{1-(-60)}}{6} \\ m=\frac{-1\pm\sqrt[]{1+60}}{6} \\ m=\frac{-1\pm\sqrt[]{61}}{6} \end{gathered}`

Hence,

`m=\frac{-1\pm\sqrt[]{61}}{6}`

The values of N, D and M are

`\begin{gathered} N=-1 \\ D=61 \\ M=6 \end{gathered}`

The values of m are

`\begin{gathered} m=\frac{-1+\sqrt[]{61}}{6}=1.13504=1.14\text{ (two decimal places)} \\ m=\frac{-1-\sqrt[]{61}}{6}=-1.46837=-1.47\text{ (two decimal places)} \end{gathered}`

Hence, the values of m in two decimal places is

`m=1.14\text{ or }-1.47\text{ (two decimal places)}`