MathDB
P31 [Algebra] - Turkish NMO 1st Round - 2005

Source:

November 2, 2013

Problem Statement

If the equation system f(x)+g(x)=0f(x)(g(x))3=0\begin{array}{rcl} f(x) + g(x) &=& 0 \\ f(x)-(g(x))^3 &=& 0 \end{array} has more than one real roots, where a,b,c,da,b,c,d are reals and f(x)=x2+ax+bf(x)=x^2 + ax+b, g(x)=x2+cx+dg(x)=x^2 + cx + d, at most how many distinct real roots can the equation f(x)g(x)=0f(x)g(x) = 0 have?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4