My missing piece

Algebra Level 3

If 3 + 1 \sqrt{3} + 1 is a root of the equation 3 x 3 + a x 2 + b x + 12 = 0 3x^3 + ax^2 + bx + 12 = 0 for rational real constants a , b a,b . What is the value of b b ?

-6 10 2 6

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Samrit Pramanik by Samrit Pramanik , 24, India

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1 solution

Govind Shukla
May 23, 2015

the given root will definitely have its conjugate. Apply the relation between co-efficient and roots of a cubic eq. to find the 3rd root; r1 r2 r3=-12/3 . Lastly, apply the equation for b; r1 r2+r2 r3+r3*r1=b/3; r1,r2,r3 are respectively the roots of the equation...enjoy

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