Manipulating expressions in the roots Quiz

1. The roots of $x^2-7x+10=0$ are $\alpha$ and $\beta$. What is $\alpha^2+\beta^2$?

• A. $29$
• B. $49$
• C. $19$
• D. $39$

2. The roots of $3x^2-x-2=0$ are $\alpha$ and $\beta$. What is $\frac1\alpha+\frac1\beta$?

• A. $\frac{3}{2}$
• B. $-\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $-\frac{3}{2}$

3. The roots of $x^2-3x+1=0$ are $\alpha$ and $\beta$. What is $\alpha^3+\beta^3$?

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

4. The roots of $x^2+4x+2=0$ are $\alpha$ and $\beta$. What is $(\alpha-\beta)^2$?

• A. $24$
• B. $16$
• C. $12$
• D. $8$

5. The roots of $x^2-4x+1=0$ are $\alpha$ and $\beta$. What is $\alpha^4+\beta^4$?

• A. $14$
• B. $194$
• C. $196$
• D. $192$