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  • Civil Engg. (GATE) 2007
  • Given that one root of the equation x3 – 10x2 + 31x – 30 ...
Multiple choice

Given that one root of the equation x3 – 10x2 + 31x – 30 = 0 is 5, the other two roots are

  1. 2 and 3

  2. 2 and 4

  3. 3 and 4

  4. – 2 and – 3

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A Correct answer
Explanation

Given root 5, divide (x^3 - 10x^2 + 31x - 30) by (x-5) to get (x^2 - 5x + 6). Factoring (x^2 - 5x + 6) gives (x-2)(x-3). Thus, the roots are 2 and 3.

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