Roots and coefficients of polynomialsAQA A-Level Further Maths: Mind map

Exam questions on Roots and coefficients of polynomials

1. The roots of the equation $x^3-4x^2+5x-7=0$ are $\alpha$, $\beta$ and $\gamma$.
   Find the value of $\frac1\alpha+\frac1\beta+\frac1\gamma$.2 marks
2. The roots of the equation $x^4-6x^3+3x^2+2x-5=0$ are $\alpha$, $\beta$, $\gamma$ and $\delta$.
   Find the value of $\alpha^2+\beta^2+\gamma^2+\delta^2$.2 marks
3. The roots of the equation $x^3+3x^2-5x+1=0$ are $\alpha$, $\beta$ and $\gamma$.
   Show that $\alpha^2+\beta^2+\gamma^2=19$.3 marks