Radix+Quadratic equation

Question

The radix of the number invovled in quadratic equation is, $x^2-10x+39=0$, if the solutions to the quadratic equation is $6$ and $9$ A. $12$ B. $13$ C. $15$ D. $9$

Answer 1

Let $ax^2 + bx +c = 0$ be a quadratic equation, then

Sum of roots $= \frac{-b}{a}$ and product of roots $= \frac{c}{a}$

$\color{red}{(6)_{ b} + (9)_{b} = (10)_{b} \Rightarrow b = 15}$

and $ (6)_{b}*(9)_{b} = (39)_{b}$ means $54 = 3b+ 9$, So $\color{blue}{b = 15}$

Comments

Nice explanation ..:)