Lesson 13.3: The Quadratic Formula — Practice Questions

1. 1. For the quadratic equation $4x^2 - 9x + 1 = 0$, what is the value of the coefficient $b$? The value is ___.

2. 2. To use the quadratic formula for $x^2 + 3x = 10$, what are the correct values for $a$, $b$, and $c$?

   • A. $a = 1, b = 3, c = 10$
   • B. $a = 1, b = 3, c = -10$
   • C. $a = 0, b = 3, c = -10$
   • D. $a = 1, b = -3, c = 10$

3. 3. After rewriting the equation $5x^2 = -4x + 2$ in standard form $ax^2+bx+c=0$, what is the value of $c$? The value is ___.

4. 4. What is the value of the coefficient $a$ in the quadratic equation $-x^2 + 6x - 5 = 0$?

   • A. 1
   • B. -1
   • C. 0
   • D. 6

5. 5. To prepare the equation $2x^2 + 5 = -3x$ for the quadratic formula, it must be rewritten in standard form. What is the value of $b$? The value is ___.

6. 6. What is the sum of the roots of the quadratic equation $x^2 + 7x + 10 = 0$? ___

7. 7. What is the product of the roots for the equation $3x^2 - 8x - 3 = 0$? ___

8. 8. For the quadratic equation $2x^2 - 9x + 4 = 0$, what are the sum and product of its roots?

   • A. Sum is $\frac{9}{2}$, Product is $2$
   • B. Sum is $-\frac{9}{2}$, Product is $2$
   • C. Sum is $9$, Product is $4$
   • D. Sum is $\frac{9}{2}$, Product is $4$

9. 9. Which quadratic equation has roots whose sum is 6 and whose product is 7?

   • A. $x^2 - 6x + 7 = 0$
   • B. $x^2 + 6x + 7 = 0$
   • C. $x^2 - 6x - 7 = 0$
   • D. $x^2 + 7x - 6 = 0$

10. 10. The sum of the roots of the equation $5x^2 + 2x - 3 = 0$ is ___. (Enter as a fraction)