Discriminant and Quadratic Formula

Find the discriminant of 2x² + 3x + 4 = 0.

• -23
• 41
• -15
• 9
• -32

Answer explanation

Correct: **-23** (b² - 4ac = 3² - 4(2)(4) = 9 - 32 = -23). Errors: **41** (added instead of subtracting 4ac), **-15** (used c=3), **9** (forgot 4ac), **-32** (ignored b²).

Find the discriminant of x² + 2x + 5 = 0.

• -16
• 9
• 20
• -4
• 4

Answer explanation

Correct: **-16** (2² - 4(1)(5) = 4 - 20 = -16). Errors: **9** (only b²), **20** (added 4ac), **-4** (wrong a=2), **4** (wrong sign).

Find the discriminant of 3x² - x + 2 = 0.

• -23
• 25
• 13
• 7
• -7

Answer explanation

Correct: **-23** ((-1)² - 4(3)(2) = 1 - 24 = -23). Errors: **25** (added 4ac), **13** (wrong b=1), **7** (miscalculation), **-7** (partial subtraction).

Find the discriminant of x² - 4x + 4 = 0.

• 0
• 16
• -16
• 8
• 4

Answer explanation

Correct: **0** ((-4)² - 4(1)(4) = 16 - 16 = 0). Errors: **16** (ignored 4ac), **-16** (subtracted incorrectly), **8** (wrong b=2), **4** (partial calculation).

Find the discriminant of 2x² + 4x + 2 = 0.

• 0
• 32
• 16
• -8
• 8

Answer explanation

Correct: **0** (4² - 4(2)(2) = 16 - 16 = 0). Errors: **32** (added 4ac), **16** (only b²), **-8** (wrong sign), **8** (miscalculation).

Find the discriminant of 9x² + 6x + 1 = 0.

• 0
• 36
• 72
• -36
• 12

Answer explanation

Correct: **0** (6² - 4(9)(1) = 36 - 36 = 0). Errors: **36** (ignored 4ac), **72** (added 4ac), **-36** (subtracted incorrectly), **12** (partial subtraction).

Find the discriminant of x² - 5x + 6 = 0.

• 1
• 49
• -1
• 25
• 24

Answer explanation

Correct: **1** ((-5)² - 4(1)(6) = 25 - 24 = 1). Errors: **49** (added 4ac), **-1** (sign error), **25** (only b²), **24** (only 4ac).

Find the discriminant of 2x² + x - 3 = 0.

• 25
• 1
• -25
• -7
• 7

Answer explanation

Correct: **25** (1² - 4(2)(-3) = 1 + 24 = 25). Errors: **1** (ignored 4ac), **-25** (sign error), **-7** (wrong c=3), **7** (partial calculation).

Find the discriminant of x² + 3x + 2 = 0.

• 1
• 13
• -1
• 9
• -9

Answer explanation

Correct: **1** (3² - 4(1)(2) = 9 - 8 = 1). Errors: **13** (added 4ac), **-1** (sign error), **9** (only b²), **-9** (wrong subtraction).

Find the discriminant of 3x² - 2x - 1 = 0.

• 16
• -8
• 8
• 4
• -4

Answer explanation

Correct: **16** ((-2)² - 4(3)(-1) = 4 + 12 = 16). Errors: **-8** (ignored negative c), **8** (partial sum), **4** (only b²), **-4** (sign error).