Question

If 3 and 1 + Ö2 are two roots of a cubic equation with rational coefficients then the equation is

• A. x³ – 5x² + 9x – 9 = 0
• B. x³–3x² – 4x + 12 = 0
• C. x³ – 5x² + 7x + 3 = 0
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

1 + $\sqrt{2}$, 1 – $\sqrt{2}$, 3sum = 5, product = 3(1 – 2) = – 3

double product = 3(1–$\sqrt{2}$+1+$\sqrt{2}$)+(1+$\sqrt{2}$)(1–$\sqrt{2}$)

= 6 + 1 – 2 = 5 eqⁿ = x³ – 5x² + 5x + 3 = 0