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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

The roots of x3−6x2+11x−6=0x^3 - 6x^2 + 11x - 6 = 0 are r1,r2,r3r_1, r_2, r_3. What is r1r2+r1r3+r2r3r_1 r_2 + r_1 r_3 + r_2 r_3?

  • A

    −6-6

  • B

    −11-11

  • C

    66

  • D

    1111

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Explanation

By Vieta's formulas for x3−6x2+11x−6x^3 - 6x^2 + 11x - 6, the sum of products of pairs equals the coefficient of xx, which is 1111.

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