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What base? (Posted on 2022-05-28) Difficulty: 3 of 5
What base will make the bold text true:

Equation: 3x2-25x+66=0
It’s solutions x1=4 and x2=9 ?

Provide your reasoning.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Another quick solution Comment 3 of 3 |
The vertex for the parabola must have x-coordinate halfway between the zeros: (4+9)/2=6.5 but the x-coordinate of the vertex is -b/(2a) so in base n we have:

(2n+5)/(2*3)=6.5

n=17

Which checks as the others have shown

  Posted by Jer on 2022-05-28 23:30:39
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