Embibe Experts Solutions for Exercise 1: Exercise

Form polynomial equations of the lowest degree, with roots as given below:$1\pm 2i,4,2$

Given that the roots of $x^3+3p{x}^2+3qx+r=0$ are in $A.P.$. Show that $2p^3-3qp+r=0$.

Solve the equation $3x^3-26x^2+52x-24=0$, given that the roots of each are in $\mathrm{G}.\mathrm{P}.$

If the roots of $x^3+3p{x}^2+3qx+r=0$ are in $\mathrm{H}.\mathrm{P}.$ show that $2q^3=r(3pq-r)$.

Solve the following equations, given that the roots of each are in $\mathrm{H}.\mathrm{P}.$$6x^3-11x^2+6x-1=0$.

Solve the equation $x^4+2x^3-5x^2+6x+2=0$ given that $1+i$ is one of its roots.

Solve the equation $2x^2+3ix+2=0$ by using general expressions for the roots of the equation.

Solve $x^4+x^3-16x^2-4x+48=0$, given that the product of two of the roots is $6$.