Solution

The correct answer is option 4.

Key Points

If one solve the quadratic equation, ax2 + bx + c
then the sum of roots of quadratic equation = −b/a

Quadratic equation x2 - 10x + 26 = 0
since 4 and 7 are the roots of the equation

∴ \(\frac{-b}{a} = \frac{(10)_r}{(1)_r} = (4)_r + (7)_r \)
r = 4 + 7 = 11

∴ Hence the correct answer is 11.

Alternate Method

In this case, it would be sufficient to take one solution and put it into the equation. Say we do it with x=4. Convert the coefficients into base 10. Let the radix be r.

x2 - 10x + 26 = 0

(4)2 – (1 × r1 + 0 × r0) × 4 + (2 × r1 + 6 × r0)=0 

16 − 4r + 2r + 6 = 0

2r = 22

r = 11