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Omni-MATH / Let a,b,c be integers. Define f(x)=ax²+bx+c. Suppose there exist pairwise distinct integers u,v,w such that f(u)=0,f(v)=0, and f(w)=2. Find the maximum possible value of the discri…

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Let a,b,ca, b, c be integers. Define f(x)=ax2+bx+cf(x)=a x^{2}+b x+c. Suppose there exist pairwise distinct integers u,v,wu, v, w such that f(u)=0,f(v)=0f(u)=0, f(v)=0, and f(w)=2f(w)=2. Find the maximum possible value of the discriminant b2−4acb^{2}-4 a c of ff.
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Let a,b,c be integers. Define f(x)=ax²+bx+c. Suppose there exist pairwise distinct integers u,v,w such that f(u)=0,f(v)=0, and f(w)=2. Find the maximum possible value of the discriminant b²−4ac of f.
Original LaTeX notation
Let $a, b, c$ be integers. Define $f(x)=a x^{2}+b x+c$. Suppose there exist pairwise distinct integers $u, v, w$ such that $f(u)=0, f(v)=0$, and $f(w)=2$. Find the maximum possible value of the discriminant $b^{2}-4 a c$ of $f$.

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task_id
a30359b0-1f27-5ad4-a971-6d94d014b4ca
task_key
test--a30359b0-1f27-5ad4-a971-6d94d014b4ca
task_revision_id
1
config / split
/ test

Official source

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