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svp [43]
2 years ago
5

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

Mathematics
1 answer:
kompoz [17]2 years ago
6 0
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}


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