Let’s solve each problem step by step.
The
discriminant of a quadratic equation in the form
>
ax² + bx + c = 0
is calculated using the formula:
>
Discriminant = b² - 4ac
We’ll go through each equation one by one, identify a, b, and c, then plug into the formula.
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1) –x² + x + 1 = 0
→ a = –1, b = 1, c = 1
Discriminant = (1)² – 4(–1)(1) = 1 + 4 =
5
2) 2x² + x + 5 = 0
→ a = 2, b = 1, c = 5
Discriminant = (1)² – 4(2)(5) = 1 – 40 =
–39
3) x² + 7x + 4 = 0
→ a = 1, b = 7, c = 4
Discriminant = (7)² – 4(1)(4) = 49 – 16 =
33
4) –x² – 3x + 2 = 0
→ a = –1, b = –3, c = 2
Discriminant = (–3)² – 4(–1)(2) = 9 + 8 =
17
5) 2x² – 4x + 1 = 0
→ a = 2, b = –4, c = 1
Discriminant = (–4)² – 4(2)(1) = 16 – 8 =
8
6) –2x² – x + 6 = 0
→ a = –2, b = –1, c = 6
Discriminant = (–1)² – 4(–2)(6) = 1 + 48 =
49
7) x² – 11x + 3 = 0
→ a = 1, b = –11, c = 3
Discriminant = (–11)² – 4(1)(3) = 121 – 12 =
109
8) –x² – 2x – 9 = 0
→ a = –1, b = –2, c = –9
Discriminant = (–2)² – 4(–1)(–9) = 4 – 36 =
–32
9) 3x² + 6x + 3 = 0
→ a = 3, b = 6, c = 3
Discriminant = (6)² – 4(3)(3) = 36 – 36 =
0
10) 13x² – 7x + 1 = 0
→ a = 13, b = –7, c = 1
Discriminant = (–7)² – 4(13)(1) = 49 – 52 =
–3
11) –x² + 6x + 7 = 0
→ a = –1, b = 6, c = 7
Discriminant = (6)² – 4(–1)(7) = 36 + 28 =
64
12) 19x² + 8x = 0 → This is same as 19x² + 8x + 0 = 0
→ a = 19, b = 8, c = 0
Discriminant = (8)² – 4(19)(0) = 64 – 0 =
64
13) 3x² – 5x – 2 = 0
→ a = 3, b = –5, c = –2
Discriminant = (–5)² – 4(3)(–2) = 25 + 24 =
49
14) –x² + 7x – 2 = 0
→ a = –1, b = 7, c = –2
Discriminant = (7)² – 4(–1)(–2) = 49 – 8 =
41
15) –4x² + 2x + 1 = 0
→ a = –4, b = 2, c = 1
Discriminant = (2)² – 4(–4)(1) = 4 + 16 =
20
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Final Answer:
1) 5
2) –39
3) 33
4) 17
5) 8
6) 49
7) 109
8) –32
9) 0
10) –3
11) 64
12) 64
13) 49
14) 41
15) 20
Parent Tip: Review the logic above to help your child master the concept of the quadratic formula and the discriminant worksheet.
