To find the discriminant of a quadratic equation, we use the formula:
Discriminant = b² - 4ac
First, make sure the equation is in standard form:
ax² + bx + c = 0 (or with any variable instead of x)
Then identify:
-
a = coefficient of the squared term
-
b = coefficient of the linear term
-
c = constant term
Plug into the formula and calculate.
Let’s go one by one:
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1) 2c² + 5c + 7 = 0
→ a = 2, b = 5, c = 7
Discriminant = 5² - 4(2)(7) = 25 - 56 =
-31
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2) y² - 4y + 9 = 0
→ a = 1, b = -4, c = 9
Discriminant = (-4)² - 4(1)(9) = 16 - 36 =
-20
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3) 7m² + 2m - 4 = 0
→ a = 7, b = 2, c = -4
Discriminant = 2² - 4(7)(-4) = 4 + 112 =
116
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4) 8x² - 7x = 0
Rewrite as: 8x² - 7x + 0 = 0 → a = 8, b = -7, c = 0
Discriminant = (-7)² - 4(8)(0) = 49 - 0 =
49
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5) 6s² + 5 = 0
Rewrite as: 6s² + 0s + 5 = 0 → a = 6, b = 0, c = 5
Discriminant = 0² - 4(6)(5) = 0 - 120 =
-120
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6) 3w² + 8w + 6 = 0
→ a = 3, b = 8, c = 6
Discriminant = 8² - 4(3)(6) = 64 - 72 =
-8
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7) 9r² - 8r - 1 = 0
→ a = 9, b = -8, c = -1
Discriminant = (-8)² - 4(9)(-1) = 64 + 36 =
100
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8) 4a² - 1 = 0
Rewrite as: 4a² + 0a - 1 = 0 → a = 4, b = 0, c = -1
Discriminant = 0² - 4(4)(-1) = 0 + 16 =
16
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9) 10t² + 6t = 0
Rewrite as: 10t² + 6t + 0 = 0 → a = 10, b = 6, c = 0
Discriminant = 6² - 4(10)(0) = 36 - 0 =
36
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10) 5n² - 9n + 2 = 0
→ a = 5, b = -9, c = 2
Discriminant = (-9)² - 4(5)(2) = 81 - 40 =
41
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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 discriminant worksheet.
