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1.(a) solve the equation $x^4-5x^3+11x^2-13x+6=0$ , given that two of its roots $p$ & $q$ are connected by the relation $3p+2q=7$

(b) solve the equation $x^4-5x^3+11x^2-13x+6=0$ which has two roots whose difference is $1$

did I need to solve these problems by taking roots $x_1,x_2,x_3,x_4$ and using the relation between roots and coefficients and the given facts. it will be then a very lengthy process.is there any alternative short process

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    Polynomials, such as these, you should always consider 1,-1,2,-2 as a chose of your roots because in most cases that I dealt with they are. If you plug in 1 as a root you see that it satisfies the condition. From there you can factor out a $(x-1)$ from the equation.2012-11-20
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    diimension: I think (in general) one would try all the factors of the constant term, here 6, so also 3,-3,6,-6 besides 1,-1 and 2,-2.2012-11-20

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