Lesson 113: Interpreting the Discriminant — Practice Questions

1. 1. How many real solutions does the quadratic equation $3x^2 - 5x + 2 = 0$ have? Enter the number of solutions: ___.

2. 2. Without solving, determine the number of real solutions for the equation $4x^2 - 12x + 9 = 0$.

   • A. 0
   • B. 1
   • C. 2
   • D. 3

3. 3. What is the value of the discriminant for the quadratic equation $x^2 + 3x + 5 = 0$? The value is ___.

4. 4. A right triangle has legs with lengths of 8 units and 15 units. What is the length of the hypotenuse? The length is ___ units.

5. 5. In a right-angled triangle, the two legs measure 7 cm and 24 cm. What is the length of the hypotenuse?

   • A. 17 cm
   • B. 25 cm
   • C. 31 cm
   • D. 50 cm

6. 6. Find the value of $k$ such that the quadratic equation $x^2 - 10x + k = 0$ has a double root. $k = $ ___

7. 7. If a quadratic equation has a double root, what does this imply about the graph of the corresponding parabola?

   • A. The parabola's vertex is on the x-axis.
   • B. The parabola opens downwards.
   • C. The parabola does not intersect the x-axis.
   • D. The parabola intersects the x-axis at two distinct points.

8. 8. The quadratic equation $4x^2 + 20x + k = 0$ has exactly one real solution. What is the value of $k$? $k = $ ___

9. 9. What is the value of the discriminant for the quadratic equation $x^2 - 6x + 9 = 0$?

   • A. 0
   • B. 36
   • C. -36
   • D. 72

10. 10. Use the Subtraction Property of Equality to solve the equation for the variable $y$. $y + 9 = 21$. $y = $ ___