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Previous Year Question (PYQs)

What is the radix of the numbers if the solution to the quadratic equation $x^2-10x+26=0$ is $x=4$ and $x=7$?




Solution

Let radix be $r$.

In base $r$,

$10=r$

$26=2r+6$

Given roots are $4$ and $7$.

Sum of roots:

$4+7=11$

For equation $x^2-10x+26=0$, sum of roots $=10$ in base $r$.

So,

$r=11$

Also, product of roots:

$4\times7=28$

And,

$26=2r+6=2(11)+6=28$

So, radix is $11$.

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