GATE CSE 2017 | Set 2 | Question: 24

Question

Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____

Comments

$x^2 -13x+36 = 0$

Roots = 5,6

Hence, $x=5,6$ will satisfy this given equation.

Putting, $x=5,$

$(5)_b * (5)_b - (13)_b*(5)_b+(36)_b=(0)_b$

Converting everything in base 10,

$25-(b+3)5+3b+6=0$

$b=8$

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roots are incorrect its should be 4 an 9 so i think question is mathematically in correct??

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roots are 4 and 9 in decimal. not in base b

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the given eqn given is in base b not in base 10

we can apply sum of roots = -b/a

product of roots = c/a

in base b, 5+6 = 13= b + 3

while in base 10, 5 + 6 =11

so, b+3 =11 => b=8 (ans)

Answer 1

Ans - 8