Equations — Practice Quiz

A Algebra cheat sheet for Equations — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. What is the value of $x$ in the equation $3x - 9 = 0$?

   • $3$
   • $-3$
   • $0$
   • $9$

   Answer: $3$

2. For the quadratic equation $2x^2 + 5x - 3 = 0$, what are the values of $a$, $b$, and $c$?

   • $a=2, b=5, c=-3$
   • $a=2, b=-5, c=3$
   • $a=2, b=5, c=3$
   • $a=-2, b=5, c=-3$

   Answer: $a=2, b=5, c=-3$

3. Which of the following quadratic equations has exactly one real root?

   • $x^2 - 4x + 4 = 0$
   • $x^2 + x + 1 = 0$
   • $x^2 - 5x + 6 = 0$
   • $2x^2 + 3x - 1 = 0$

   Answer: $x^2 - 4x + 4 = 0$

4. What is the sum of the roots of the quadratic equation $3x^2 - 6x + 2 = 0$?

   • $2$
   • $-2$
   • $\frac{2}{3}$
   • $-\frac{2}{3}$

   Answer: $2$

5. What is the product of the roots of the quadratic equation $x^2 + 7x - 10 = 0$?

   • $-10$
   • $10$
   • $7$
   • $-7$

   Answer: $-10$

6. Find the roots of the equation $x^2 - 5x + 6 = 0$.

   • $x=2, x=3$
   • $x=-2, x=-3$
   • $x=1, x=6$
   • $x=-1, x=-6$

   Answer: $x=2, x=3$

7. If the discriminant of a quadratic equation is $16$, how many real roots does the equation have?

   • $0$
   • $1$
   • $2$
   • $3$

   Answer: $2$

8. A quadratic equation has roots $x_1 = 2$ and $x_2 = -3$. Which of the following could be the equation?

   • $x^2 + x - 6 = 0$
   • $x^2 - x - 6 = 0$
   • $x^2 - 5x - 6 = 0$
   • $x^2 + 5x - 6 = 0$

   Answer: $x^2 + x - 6 = 0$

9. Consider the equation $kx^2 - 4x + 1 = 0$. For what value of $k$ will the equation have exactly one real root?

   • $k=4$
   • $k=0$
   • $k=16$
   • $k=-4$

   Answer: $k=4$

10. Find the roots of the equation $x^2 + 2x + 5 = 0$.

    • $-1 \pm 2i$
    • $1 \pm 2i$
    • $-1 \pm 4i$
    • $1 \pm 4i$

    Answer: $-1 \pm 2i$