Question

Find the constant term of a cubic equation $b^3+m{b}^2+nb+c$ given that it has 2 roots which are the same as that of the quadratic equation $d{x}^2-ex+f$ and the third root as the sum of the roots of the quadratic equation The sum of the roots of the quadratic equation = 13 and product =40

• A. 365
• B. 380
• C. 520
• D. None of these

Answer 1

The correct option is D None of these

Let the roots of the quadratic equation be p $\&$ q ,p+q=13, p$\times$q=40

p=8 q=5.

The roots of the cubic equation are 8,5 and 13

The cubic equation can be represented as (b-8)(b-5)(b-13)=0

Constant term =$(-1{)}^3(8\times 5\times 13)=-520$