Question

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

Answer 1

Answer:

7 and -2

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:

$m=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

This gives:

$\begin{gathered} m=\dfrac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(-14)}}{2\times1} \\ =\dfrac{5\pm\sqrt[]{25+56}}{2} \\ =\dfrac{5\pm\sqrt[]{81}}{2} \\ m=\dfrac{5\pm9}{2} \end{gathered}$

Threfore:

$\begin{gathered} m=\dfrac{5+9}{2}\text{ or }m=\dfrac{5-9}{2} \\ m=\dfrac{14}{2}\text{ or }m=\dfrac{-4}{2} \\ m=7\text{ or }m=-2 \end{gathered}$

The zeros of the function are 7 and -2.