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What base? (Posted on 2022-05-28)

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.)

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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