Sum and product of roots Quiz

1. The roots of $x^2-5x+3=0$ are $\alpha$ and $\beta$. Find $\alpha^2+\beta^2$.

• A. $25$
• B. $19$
• C. $31$
• D. $22$

2. The roots of $2x^2+3x-4=0$ are $\alpha$ and $\beta$. Find $\alpha\beta$.

• A. $-\frac32$
• B. $\frac32$
• C. $-4$
• D. $-2$

3. The roots of $x^2-2x+5=0$ are $\alpha$ and $\beta$. Which equation has roots $3\alpha$ and $3\beta$?

• A. $x^2-6x+15=0$
• B. $x^2+6x+45=0$
• C. $x^2-6x+45=0$
• D. $x^2-2x+45=0$

4. The roots of $x^2-3x+1=0$ are $\alpha$ and $\beta$. Find $\alpha^3+\beta^3$.

• A. $18$
• B. $24$
• C. $27$
• D. $30$

5. The roots of $x^2-4x+2=0$ are $\alpha$ and $\beta$. Find $\dfrac1\alpha+\dfrac1\beta$.

• A. $2$
• B. $\frac12$
• C. $4$
• D. $-2$