[tex]ax^2+bx+c=0[/tex] if m and n are zeros, then: [tex]m+n=\dfrac{-b}{a}\ and\ mn=\dfrac{c}{a}[/tex] We have: [tex]ax^2-5x+c=0\to b=-5\\\\m+n=mn=10[/tex] substitute [tex]m+n=\dfrac{-(-5)}{a};\ mn=\dfrac{c}{a}\\\\ \left\{\begin{array}{ccc}\dfrac{5}{a}=10&\to a=\dfrac{1}{2}\\\\\dfrac{c}{a}=10\end{array}\right[/tex] substitute the value of a to the second equation: [tex]\dfrac{c}{\frac{1}{2}}=10\\\\2c=10\ \ \ |:2\\\\c=5[/tex]
