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1. If A, b, and c are the roots of the equation 2x^3-6x^2-15x-3=0, then find (1/(a^2)) + (1/(b^2)) + (1/(c^2))

2. Let a, b, c be the roots of the equation 2x^3+4x^2-5x-3=0. Build a cubic equation which has roots ab, bc, ac

3. The polynomials x^3-ax^2-2x-1 and x^3-3x-2 have a common root. Find all possible values of a.

 Feb 15, 2021
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1. 1/a^2 + 1/b^2 + 1/c^2 = 11/8.

 

2. (x - ab)(x - bc)(x - ac) = 6x^3 - 20x^2 + 8x - 4.

 

3. The possible values of a are 1 and 3.

 Feb 15, 2021

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