Q) If a,b,c are the roots of the equation x*3+px+q=0,then find out the value of determinant 1+a 1 11 1+b - Maths - Determinants

Question

Q) If a,b,c are the roots of the equation x*3+px+q=0,then find
out the value of determinant 1+a 1 11 1+b 11 1 1+c

Vipin Verma · Accepted Answer

The given determinant is :1+a1111+b1111+c =(1+a)(1+b)(1+c)-1-a-b-c=ab+bc+ca+abcAs the cubic equation is :x3+px +q =0 [standard form is Ax3+Bx2 +Cx +D = 0] sum of roots =-BAhence  (a+b+c) = 0product of roots taking two at a time =CA Hence (ab+bc+ca)=pProduct of roots =DAHence abc =-qHence ab+bc+ca+abc =p-q (ans)

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Q) If a,b,c are the roots of the equation x*3+px+q=0,then find out the value of determinant.1+a 1 11 1+b 11 1 1+c.