Lali_miani

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These are questions asked by Lali_miani

Determine the polynomials P∈R₃ [X] such that P (-1) = - 18 and whose remainders in the Euclidean division by X-1, X-2 and X-3 are equal to 6.

I have the polynomial :P=X⁴+X³+aX²+√2X+b

Determine a and b so that (1 + i) is zero of P; then calculate all the zeros of P

I have an equation E:=2*x^(7) -x^(6) -4*x^(5) -15*x^(4) -14 x^(3)+19*x^(2) +28*x+30

I want to the list of solutions which are real numbers (resp. which have a strictly positive imaginary part); can anyone help me !

i want to know the sign of all the coefficient of CharacteristicPolynomial of such matrix, can anyone help me to do this ?

calcul_determinant.mw

 

 


 

eqs := [II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c];

[II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c]

(1)

Sol := {DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B};

{DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B}

(2)

Inter := [B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), E = lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) and lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) = lambda[2]*(lambda[3]+mu+gamma[t])/beta+lambda[3]-lambda[1]*(lambda[3]+mu+gamma[t])*C*B/beta];

[B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), false]

(3)

simplify(eval(eqs, eval[recurse](Sol, Inter)))

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received Inter

 

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