GATE | GATE CS Mock 2018 | Set 2 | Question 32

What is the radix of the number if the solution to quadratic equation x^2 − 10x + 31 = 0 is x = 5 and x = 8?

(A) 10
(B) 8
(C) 5
(D) 13


Answer: (D)

Explanation: If equation ax^2 + bx + c = 0, then sum of roots = -b/a and product of equations = c/a.
Given equation x^2 − 10x + 31 = 0 and roots are 5 and 8. Therefore,
sum of roots = -b/a = -(-10)/1 = (10)b = 5b + 8b implies b = 13.

Also, product of roots = c/a = 31/1 = (31)b = 5b * 8b implies b = 13.

Answer is 13.

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