Forming quadratic equations with new roots Quiz

1. $x^2-5x+3=0$ has roots $\alpha,\beta$. Which equation has roots $\frac1\alpha,\frac1\beta$?

• A. $x^2-5x+3=0$
• B. $3x^2-5x+1=0$
• C. $3x^2+5x+1=0$
• D. $x^2-\frac53x+3=0$

2. $x^2-6x+2=0$ has roots $\alpha,\beta$. Which equation has roots $\alpha^3,\beta^3$?

• A. $x^2-216x+8=0$
• B. $x^2-180x+2=0$
• C. $x^2-36x+8=0$
• D. $x^2-180x+8=0$

3. $x^2-8x+4=0$ has roots $\alpha,\beta$. Which equation has roots $\frac{1}{2\alpha},\frac{1}{2\beta}$?

• A. $16x^2-16x+1=0$
• B. $x^2-x+16=0$
• C. $4x^2-8x+1=0$
• D. $16x^2-4x+1=0$

4. $x^2+px+q=0$ ($q\neq0$) has roots $\alpha,\beta$. Which equation has roots $\frac1\alpha,\frac1\beta$?

• A. $x^2-px+q=0$
• B. $px^2+qx+1=0$
• C. $qx^2+px+1=0$
• D. $qx^2-px+1=0$

5. $x^2-x-1=0$ has roots $\alpha,\beta$. Which equation has roots $\alpha^2,\beta^2$?

• A. $x^2-x+1=0$
• B. $x^2-3x+1=0$
• C. $x^2-3x-1=0$
• D. $x^2+3x+1=0$