Discussion

Explanation:

(3 + 2√2) is a root of the equation ax² + bx + c = 0 whose coefficients are integers
⇒ Since coefficients are rational the other root will be (3 - 2√2)

∴ Sum of roots = 6 = -b/a
⇒ b = -6a   …(1)

∴ product of roots = 1 = c/a
⇒ c = a   …(2)

(4 + 2√3) is a root of the equation ay² + my + n = 0 whose coefficients are integers
⇒ Since coefficients are rational the other root will be (4 - 2√3)

∴ Sum of roots = 8 = -m/a
⇒ m = -8a   …(3)

∴ product of roots = 4 = n/a
⇒ n = 4a   …(4)

Now, $\left(\frac{\mathrm{b}}{\mathrm{m}}+\frac{\mathrm{c}-2\mathrm{b}}{\mathrm{n}}\right)$ 

= $\left(\frac{-6\mathrm{a}}{-8\mathrm{a}}+\frac{\mathrm{a}+12\mathrm{a}}{4\mathrm{a}}\right)$

= $\frac{3}{4}+\frac{13}{4}$ = 4

Hence, option (c).

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