Roots of polynomialsEdexcel A-Level Further Maths: Mind map

Exam questions on Roots of polynomials

1. The cubic equation $2x^3-6x^2+3x+5=0$ has roots $\alpha$, $\beta$ and $\gamma$.
   Find the value of $\frac1\alpha+\frac1\beta+\frac1\gamma$.2 marks
2. The quartic equation $x^4+2x^3-7x^2+4x-3=0$ has roots $\alpha$, $\beta$, $\gamma$ and $\delta$.
   Find the value of $\alpha^2+\beta^2+\gamma^2+\delta^2$.2 marks
3. The cubic equation $x^3+3x^2-5x+2=0$ has roots $\alpha$, $\beta$ and $\gamma$.
   Find the value of $(3+\alpha)(3+\beta)(3+\gamma)$.3 marks