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 apply this to each equation. Remember: if the variable is not “x”, that’s okay — just treat it like x. For example, in “2c² + 5c + 7 = 0”, we have:
- a = 2
- b = 5
- c = 7
---
1) 2c² + 5c + 7 = 0
a = 2, b = 5, c = 7
Discriminant = (5)² - 4(2)(7) = 25 - 56 =
-31
---
2) y² - 4y + 9 = 0
a = 1, b = -4, c = 9
Discriminant = (-4)² - 4(1)(9) = 16 - 36 =
-20
---
3) 7m² + 2m - 4 = 0
a = 7, b = 2, c = -4
Discriminant = (2)² - 4(7)(-4) = 4 + 112 =
116
---
4) 8x² - 7x = 0
This is the same as 8x² - 7x + 0 = 0 → so c = 0
a = 8, b = -7, c = 0
Discriminant = (-7)² - 4(8)(0) = 49 - 0 =
49
---
5) 6s² + 5 = 0
Same as 6s² + 0s + 5 = 0 → b = 0
a = 6, b = 0, c = 5
Discriminant = (0)² - 4(6)(5) = 0 - 120 =
-120
---
6) 3w² + 8w + 6 = 0
a = 3, b = 8, c = 6
Discriminant = (8)² - 4(3)(6) = 64 - 72 =
-8
---
7) 9t² - 8t - 1 = 0
a = 9, b = -8, c = -1
Discriminant = (-8)² - 4(9)(-1) = 64 + 36 =
100
---
8) 4z² - 1 = 0
Same as 4z² + 0z - 1 = 0 → b = 0
a = 4, b = 0, c = -1
Discriminant = (0)² - 4(4)(-1) = 0 + 16 =
16
---
9) 10t² + 6t = 0
Same as 10t² + 6t + 0 = 0 → c = 0
a = 10, b = 6, c = 0
Discriminant = (6)² - 4(10)(0) = 36 - 0 =
36
---
10) 5n² - 9n + 2 = 0
a = 5, b = -9, c = 2
Discriminant = (-9)² - 4(5)(2) = 81 - 40 =
41
---
Final Answer:
1) -31
2) -20
3) 116
4) 49
5) -120
6) -8
7) 100
8) 16
9) 36
10) 41
Parent Tip: Review the logic above to help your child master the concept of the quadratic formula and the discriminant worksheet.
