Let's play quadratics

Algebra Level 3

Ada and Byron play a game. First, Ada chooses a non-zero real number $a$ and announces it. Then Byron chooses a non-zero real number $b$ and announces it. Then Ada chooses a non-zero real number $c$ and announces it. Finally, Byron chooses a quadratic polynomial whose three coefficients are $a, b, c$ in some order. Suppose that Byron wins if the quadratic polynomial has a real root and Ada wins otherwise. Determine which player has a winning strategy.

Byron Equal game Ada

1 solution

X X
Dec 3, 2018

First, if Ada choose a positive/negative number for $a$ , then Byron chooses a negative/positive number for $b$ .

Then, no matter what Ada choose for $c$ , Bryon can let the quadratic polynomial be $ax^2+cx+b$ , then the discriminant will be $c^2-4ab$ . $ab$ negative and $c^2$ is positive, so $c^2-4ab>0$ , which states that it has real roots.

Hence, Byron has a winning strategy.

Sir, can you please post a solution for this: https://brilliant.org/problems/confusing-question-no-way-out/ ; I am very confused

Jake Tricole - 2 years ago

Let's play quadratics

1 solution

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