f the equations x³+10x²+ax+b=0 and x²+ 4x²+ax+c=0 have two roots in common, then the product of uncommon roots of two equations is

Factoring the first polynomial by grouping yields (x + 1)(x^2 + 9x + b) = 0, so its roots are -1 and the roots of x^2 + 9x + b. The second polynomial is (x + 1)(x + 3)(x + c) = 0, so its roots are -1, -3, and -c. For the equations to share exactly two roots, the shared roots must be -1 and -3, which means b equals (-3)(-8) = 24 and c equals 3. The roots that are not shared are the third root of the first equation, -8, and the third root of the second equation, -3. Their product is (-8)(-5) = 40.

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