Concept
To write an equation for given roots, let x variable represent the solutions
Therefore,
x = 8 and x = -1/2
x - 8 = 0 and x + 1/2 = 0
x - 8 and x + 1/2 are factors.
[tex]\text{Next, multiply the two factors, then equate it to zero.}[/tex]Next, multiply the two roots to find the equation.
[tex]\begin{gathered} (x\text{ - 8) x (x + }\frac{1}{2}\text{ ) = 0} \\ x^2\text{ + }\frac{1}{2}x\text{ }-\text{ 8x - 8 }\times\text{ }\frac{1}{2}\text{ = 0} \\ x^2\text{ + }\frac{1}{2}x\text{ - 8x - }\frac{8}{2}\text{ = 0} \\ x^2\text{ - }\frac{7}{2}x\text{ - 4 = 0} \end{gathered}[/tex]Final answer
[tex]x^2\text{ - }\frac{7}{2}x\text{ - 4 = 0}[/tex]
