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

Question

If the equations  x3 + 10x2 + ax + b  =  0  and  x3 + 4x2 + ax + c  =  0  have two roots in common, then the product of uncommon roots of two equations is:
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Solution 1

The given equations are:

x³ + 10x² + ax + b = 0 ----(1)

x³ + 4x² + ax + c = 0 ----(2)

Given that these two equations have two roots in common, let's denote these common roots as p and q. The third root of equation (1) is r and the third root of equation (2) is s.

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