Verified answer

a + 2b = [4, -1] which has magnitude √(4² + 1²) = √17.

So in order to scale this vector down to a unit, you must divide by +/-√17. This can be positive or negative (1 and -1 are the units in the ring of real numbers).

So, you want answer 3.

Or directly, in a few lines:

λ(a+2b) is unit vector <=> magnitude of λ([4,-1]) = 1

<=> magnitude of [4λ,-λ] = 1

<=> 4²λ²+(-1)²λ² = 1

<=> 17λ² = 1

<=> λ² = 1/17

<=> λ = +/- 1/√17