Name: ______________________________
Common Core Algebra 9H – Nature of the Roots
Date: _____________
HW #66
1. For which quadratic equation are the roots irrational?
(a) 2x 2  7x  3  0
(b) 2x 2  6x  3  0
(c) 2x 2  5x  3  0
(d) 2x 2  x  3  0
2. The roots of the equation x 2  3x  2  0
(a) real, irrational, and unequal
(b) real, rational, and equal
(c) real, rational, and unequal
(d) imaginary
3. If the graph of ax2  bx  c lies entirely above the x-axis, then the roots of ax 2  bx  c  0 are
(a) rational and unequal
(b) rational and equal
(c) irrational
(d) imaginary (no real roots)
Without solving, determine the number of real solutions for each quadratic equation.
Which equation(s) would be able to be solved by factoring?
4. 𝑏 2 − 4𝑏 + 3 = 0
5. 2𝑛2 + 7 = −4𝑛 + 5
6. 𝑥 − 3𝑥 2 = 5 + 2𝑥– 𝑥 2
7. 4𝑞 + 7 = 𝑞 2 − 5𝑞 + 1
8. Describe the nature of the roots of the equations below:
a. 2x2 – x = 4
b. 5x2 – 2x = 3
9. Describe both the number of real solutions and the discriminant based off of the following graphs.
A
B
C
D
Mixed Review:
1. Solve the following: 2x2 – 3x – 5 = 0 (Hint: Use discriminant to determine which method to use)
2. In the function f(x) = (x – 4)2 + 7, the minimum value occurs when x is ____________.