Mathematics
Algebra
For x² + 4x + 3 = 0, what does the discriminant indicate?
A. Two non-real complex roots
B. One repeated real root
C. Two distinct real roots
D. 0
Correct Answer: C
D=16-4(3)=4; its sign determines root type.
Mathematics
Algebra
For x² + 3x + 2 = 0, what does the discriminant indicate?
A. 0
B. Two distinct real roots
C. Two non-real complex roots
D. One repeated real root
Correct Answer: B
D=9-4(2)=1; its sign determines root type.
Mathematics
Algebra
For x² + 2x + 1 = 0, what does the discriminant indicate?
A. 0
B. Two distinct real roots
C. Two non-real complex roots
D. One repeated real root
Correct Answer: D
D=4-4(1)=0; its sign determines root type.
Mathematics
Algebra
Solve: x² − 78x + 1325 = 0.
A. x = −25 or x = −53
B. x = 1325
C. x = 25 or x = 53
D. x = 78
Correct Answer: C
Factor: (x-25)(x-53)=0.
Mathematics
Algebra
Solve: x² − 75x + 1224 = 0.
A. x = 75
B. x = 1224
C. x = 24 or x = 51
D. x = −24 or x = −51
Correct Answer: C
Factor: (x-24)(x-51)=0.
Mathematics
Algebra
Solve: x² − 72x + 1127 = 0.
A. x = 72
B. x = 1127
C. x = −23 or x = −49
D. x = 23 or x = 49
Correct Answer: D
Factor: (x-23)(x-49)=0.
Mathematics
Algebra
Solve: x² − 69x + 1034 = 0.
A. x = −22 or x = −47
B. x = 22 or x = 47
C. x = 69
D. x = 1034
Correct Answer: B
Factor: (x-22)(x-47)=0.
Mathematics
Algebra
Solve: x² − 66x + 945 = 0.
A. x = 66
B. x = 21 or x = 45
C. x = −21 or x = −45
D. x = 945
Correct Answer: B
Factor: (x-21)(x-45)=0.
Mathematics
Algebra
Solve: x² − 63x + 860 = 0.
A. x = 63
B. x = −20 or x = −43
C. x = 860
D. x = 20 or x = 43
Correct Answer: D
Factor: (x-20)(x-43)=0.
Mathematics
Algebra
Solve: x² − 60x + 779 = 0.
A. x = −19 or x = −41
B. x = 60
C. x = 779
D. x = 19 or x = 41
Correct Answer: D
Factor: (x-19)(x-41)=0.
Mathematics
Algebra
Solve: x² − 57x + 702 = 0.
A. x = 57
B. x = 702
C. x = −18 or x = −39
D. x = 18 or x = 39
Correct Answer: D
Factor: (x-18)(x-39)=0.
Mathematics
Algebra
Solve: x² − 54x + 629 = 0.
A. x = 54
B. x = 17 or x = 37
C. x = 629
D. x = −17 or x = −37
Correct Answer: B
Factor: (x-17)(x-37)=0.
Mathematics
Algebra
Solve: x² − 51x + 560 = 0.
A. x = 16 or x = 35
B. x = 560
C. x = 51
D. x = −16 or x = −35
Correct Answer: A
Factor: (x-16)(x-35)=0.
Mathematics
Algebra
Solve: x² − 48x + 495 = 0.
A. x = 48
B. x = −15 or x = −33
C. x = 15 or x = 33
D. x = 495
Correct Answer: C
Factor: (x-15)(x-33)=0.
Mathematics
Algebra
Solve: x² − 45x + 434 = 0.
A. x = −14 or x = −31
B. x = 45
C. x = 14 or x = 31
D. x = 434
Correct Answer: C
Factor: (x-14)(x-31)=0.
Mathematics
Algebra
Solve: x² − 42x + 377 = 0.
A. x = 13 or x = 29
B. x = 42
C. x = 377
D. x = −13 or x = −29
Correct Answer: A
Factor: (x-13)(x-29)=0.
Mathematics
Algebra
Solve: x² − 39x + 324 = 0.
A. x = 12 or x = 27
B. x = 324
C. x = 39
D. x = −12 or x = −27
Correct Answer: A
Factor: (x-12)(x-27)=0.
Mathematics
Algebra
Solve: x² − 36x + 275 = 0.
A. x = 275
B. x = 36
C. x = −11 or x = −25
D. x = 11 or x = 25
Correct Answer: D
Factor: (x-11)(x-25)=0.
Mathematics
Algebra
Solve: x² − 33x + 230 = 0.
A. x = 33
B. x = 230
C. x = 10 or x = 23
D. x = −10 or x = −23
Correct Answer: C
Factor: (x-10)(x-23)=0.
Mathematics
Algebra
Solve: x² − 30x + 189 = 0.
A. x = 9 or x = 21
B. x = −9 or x = −21
C. x = 30
D. x = 189
Correct Answer: A
Factor: (x-9)(x-21)=0.