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=(-b)/(a)\ and\ mn=(c)/(a)`
We have:

`ax^2-5x+c=0\to b=-5\\\\m+n=mn=10`
substitute

`m+n=(-(-5))/(a);\ mn=(c)/(a)\\\\ \left\{\begin{array}{ccc}(5)/(a)=10&\to a=(1)/(2)\\\\(c)/(a)=10\end{array}\right`
substitute the value of a to the second equation:

`(c)/((1)/(2))=10\\\\2c=10\ \ \ |:2\\\\c=5`

Answer:
`\boxed{a=(1)/(2);\ c=5}`