Question

If m and n are zeros of ax2-5x+c, find a and c when m+n=mn=10

Answer 1

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

Answer:  $\boxed{a=\dfrac{1}{2};\ c=5}$