Roots and coefficients of polynomials

Roots and coefficients of polynomials Quiz

Spec D1–D2 · AQA A-Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

1. What is the sum of the roots of $2x^2-5x+3=0$ ?
- A. $-\frac52$
- B. $\frac52$
- C. $\frac32$
- D. $-\frac32$
2. The roots of $x^3+2x^2-7x+4=0$ are $\alpha,\beta,\gamma$ . What is $\alpha\beta\gamma$ ?
- A. $4$
- B. $7$
- C. $-7$
- D. $-4$
3. The roots of $2x^4-3x^3+x^2-5x+8=0$ are $\alpha,\beta,\gamma,\delta$ . What is $\alpha\beta\gamma\delta$ ?
- A. $4$
- B. $-4$
- C. $\frac52$
- D. $-\frac52$
4. The roots of $x^3-3x^2+4x-1=0$ are $\alpha,\beta,\gamma$ . What is the sum of the roots of the equation with roots $\alpha+2$ , $\beta+2$ , $\gamma+2$ ?
- A. $5$
- B. $3$
- C. $9$
- D. $12$
5. $\sum\alpha=5$ and $\sum\alpha\beta=4$ . What is $\alpha^2+\beta^2+\gamma^2$ ?
- A. $33$
- B. $17$
- C. $21$
- D. $9$