1968 AHSME Problems/Problem 13

Problem

If $m$ and $n$ are the roots of $x^2+mx+n=0 ,m \ne 0,n \ne 0$ , then the sum of the roots is:

$\text{(A) } -\frac{1}{2}\quad \text{(B) } -1\quad \text{(C) } \frac{1}{2}\quad \text{(D) } 1\quad \text{(E) } \text{undetermined}$

Solution

By Vieta's Theorem, $mn = n$ and $-(m + n) = m$ . Dividing the first equation by $n$ gives $m = 1$ . Multiplying the 2nd by -1 gives $m + n = -m$ . The RHS is -1, so the answer is $\fbox{B}$

1968 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1968 AHSME Problems/Problem 13

Problem

Solution

See also