Question

Quadratic formula to find the zeros5. m^2-5m-14=0

Answer 1

7 and -2

Step-by-step explanation:

Given the quadratic equation:

`m^2-5m-14=0`

Comparing with the general form of a quadratic equation:

`\begin{gathered} ax^2+bx+c=0 \\ a=1,b=-5,c=-14 \end{gathered}`

Substitute these into the quadratic formula below:

`m=(-b\pm√(b^2-4ac) )/(2a)`

This gives:

`\begin{gathered} m=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(-14)}}{2*1} \\ =\frac{5\pm\sqrt[]{25+56}}{2} \\ =\frac{5\pm\sqrt[]{81}}{2} \\ m=(5\pm9)/(2) \end{gathered}`

Threfore:

`\begin{gathered} m=(5+9)/(2)\text{ or }m=(5-9)/(2) \\ m=(14)/(2)\text{ or }m=(-4)/(2) \\ m=7\text{ or }m=-2 \end{gathered}`

The zeros of the function are 7 and -2.