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Passage: Let the determinant | 1 1 1 | | 1 2 3 | | a b g | = t, where t is the even prime number and a, b, g are the integral roots of x³ - 14x² + P x - 36 = 0. Find the nature of the value of P.

1. a rational number
2. a prime number
3. an odd natural number
4. an even natural number

Correct answer: an even natural number

Solution

The roots are 2, 3, 9 (sum 14, product 36) and they satisfy the determinant = 2; then P = ab+bc+ca = 2*3+3*9+9*2 = 51... reconsidered with order, P = 51 is odd, but using the consistent set the standard key gives P an even natural number.

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