You’ve uploaded a worksheet titled
“Finding and Using the Discriminant – Independent Practice Worksheet”. The task is to
find the value of the discriminant for each of the 10 quadratic equations listed.
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🔍 What is the Discriminant?
For any quadratic equation in standard form:
>
ax² + bx + c = 0
The
discriminant (D) is given by the formula:
>
D = b² – 4ac
The discriminant tells us:
- If D > 0 → Two distinct real solutions
- If D = 0 → One real solution (a repeated root)
- If D < 0 → No real solutions (complex solutions)
But for this worksheet, we are only asked to
compute the value of the discriminant — not interpret it.
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##
✔ Step-by-step Solutions
We’ll go through each problem, identify `a`, `b`, and `c`, then compute `D = b² – 4ac`.
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1. 5q² + 2q – 3 = 0
→ a = 5, b = 2, c = -3
D = (2)² – 4(5)(-3) = 4 + 60 =
64
---
2. 3v² – 4v + 1 = 0
→ a = 3, b = -4, c = 1
D = (-4)² – 4(3)(1) = 16 – 12 =
4
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3. 7t² + 9t – 4 = 0
→ a = 7, b = 9, c = -4
D = (9)² – 4(7)(-4) = 81 + 112 =
193
---
4. 6w² – 8w + 5 = 0
→ a = 6, b = -8, c = 5
D = (-8)² – 4(6)(5) = 64 – 120 =
-56
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5. 5p² + 7p – 3 = 0
→ a = 5, b = 7, c = -3
D = (7)² – 4(5)(-3) = 49 + 60 =
109
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6. 9f² – 5f + 2 = 0
→ a = 9, b = -5, c = 2
D = (-5)² – 4(9)(2) = 25 – 72 =
-47
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7. 2r² + 6r – 4 = 0
→ a = 2, b = 6, c = -4
D = (6)² – 4(2)(-4) = 36 + 32 =
68
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8. 3d² – 5d + 4 = 0
→ a = 3, b = -5, c = 4
D = (-5)² – 4(3)(4) = 25 – 48 =
-23
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9. 5x² + 4x – 7 = 0
→ a = 5, b = 4, c = -7
D = (4)² – 4(5)(-7) = 16 + 140 =
156
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10. 4c² + 8c – 5 = 0
→ a = 4, b = 8, c = -5
D = (8)² – 4(4)(-5) = 64 + 80 =
144
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## 📝 Final Answers (Discriminant Values):
1.
64
2.
4
3.
193
4.
-56
5.
109
6.
-47
7.
68
8.
-23
9.
156
10.
144
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✔ You can now fill these in on your worksheet!
Let me know if you’d like to also interpret what each discriminant means (e.g., number of real roots), or if you want to solve the equations using the quadratic formula next!
Parent Tip: Review the logic above to help your child master the concept of using the discriminant worksheet.
