Question6. For how many different ordered pairs of nonnegative integers $(a, b)$ do $x^{2}-a x+b=0$ and $x^{2}-b x+a=0$ both have only integer roots? lease do not include unit in your answer. Integer or Finite Decimal $\qquad$ (Integer or finite decimal only.) Please click here to view the instructions to enter your answers.

Studdy Solution
Count the valid ordered pairs $(a, b)$ : - $(0, 0)$ - $(1, 1)$ - $(2, 2)$ - $(2, 0)$ - $(0, 2)$
There are 5 valid ordered pairs.
The number of different ordered pairs $(a, b)$ is:
$\boxed{5}$

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