Multiple choice

If (b - 6) is one root of the quadratic equation x2 - 6x + b = 0, where b is an integer, then what is the maximum value of b2?

  1. 36

  2. 49

  3. 64

  4. 81
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If (b-6) is a root, then (b-6)^2 - 6(b-6) + b = 0. b^2 - 12b + 36 - 6b + 36 + b = 0. b^2 - 17b + 72 = 0. (b-8)(b-9) = 0. So b=8 or b=9. Max b^2 = 9^2 = 81.

AI explanation

Substitute the root (b - 6) into the quadratic equation x^2 - 6x + b = 0 to get (b - 6)^2 - 6(b - 6) + b = 0. Expanding and simplifying this gives b^2 - 12b + 36 - 6b + 36 + b = 0, which reduces to b^2 - 17b + 72 = 0. Factoring the quadratic yields (b - 8)(b - 9) = 0, meaning b can be 8 or 9. The maximum value among these integers is 9, making the maximum value of b^2 equal to 81.

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