quadratic

if x² -xcos(A+B)+1 is a factor of the expression

2x⁴+4x³sinAsinB-x²( cos 2A+cos 2B)+4xcosAcosB-2

Then find the other factor.

2 Answers

2x^{2}+2x\cos \left(A-B \right)-2

sum of roots of 1st eqtn is cos(A+B) = (x1+x2)

Product is 1=x1 x2

producct of 2nd equation's roots is -1 = (x1.x2.x3.x4)

sum of the 2nd equation;s roots is -2sinAsinB=(x1+x2+x3+x4)

now find x3+x4 and x3.x4

thus find the equation (quadratic) with roots x3 and x4

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