Respuesta :
Answer:
Case 1: a = 1.5, b = 2, c = -3
[tex]D = 22[/tex]
Case 2: a = 2.3, b = -4, c = 1
[tex]D = 6.8[/tex]
Case 3: a = 3.7, b = 9, c = -4
[tex]D = 140.2[/tex]
Case 4: a = 4.6, b = -8, c = 5
[tex]D = -28[/tex]
Case 5: a = 5.5, b = 7, c = -3
[tex]D = 115[/tex]
Case 6: a = 6.9, b = -5, c = 2
[tex]D = -30.2[/tex]
Case 7: a = 7.2, b = 6, c = -4
[tex]D = 151.2[/tex]
Case 8: a = 8.3, b = -3, c = 4
[tex]D = -123.8[/tex]
Case 9: a = 9.9, b = 4, c = -7
[tex]D = 293.2[/tex]
Case 10: a = 10.4, b = 8, c = -5
[tex]D = 272[/tex]
Step-by-step explanation:
For all second order polynomial, the discriminant is equal to:
[tex]D = b^{2}-4\cdot a \cdot c[/tex]
Case 1: a = 1.5, b = 2, c = -3
[tex]D = 22[/tex]
Case 2: a = 2.3, b = -4, c = 1
[tex]D = 6.8[/tex]
Case 3: a = 3.7, b = 9, c = -4
[tex]D = 140.2[/tex]
Case 4: a = 4.6, b = -8, c = 5
[tex]D = -28[/tex]
Case 5: a = 5.5, b = 7, c = -3
[tex]D = 115[/tex]
Case 6: a = 6.9, b = -5, c = 2
[tex]D = -30.2[/tex]
Case 7: a = 7.2, b = 6, c = -4
[tex]D = 151.2[/tex]
Case 8: a = 8.3, b = -3, c = 4
[tex]D = -123.8[/tex]
Case 9: a = 9.9, b = 4, c = -7
[tex]D = 293.2[/tex]
Case 10: a = 10.4, b = 8, c = -5
[tex]D = 272[/tex]
The question is:
Find the value of the discriminant for all the following equations:
1. 5q² + 2q - 3 = 0
2. 3u² - 4u + 1 = 0
3. 7s² + 9s - 4 = 0
4. 6w² - 8w + 5 = 0
5. 5p² + 7p - 3 = 0
6. 9f² - 5f + 2 = 0
7. 2n² + 6n - 4 = 0
8. 3d² - 3d + 4 = 0
9. 9v² + 4v - 7 = 0
10. 4c² + 8c - 5 = 0
Answer:
1. 5q² + 2q - 3 = 0
Discriminant is 64
2. 3u² - 4u + 1 = 0
Discriminant is 4
3. 7s² + 9s - 4 = 0
Discriminant is 193
4. 6w² - 8w + 5 = 0
Discriminant is -56
5. 5p² + 7p - 3 = 0
Discriminant is 109
6. 9f² - 5f + 2 = 0
Discriminant is -47
7. 2n² + 6n - 4 = 0
Discriminant is 68
8. 3d² - 3d + 4 = 0
Discriminant is -39
9. 9v² + 4v - 7 = 0
Discriminant is 268
10. 4c² + 8c - 5 = 0
Discriminant is 144.
Step-by-step explanation:
The quadratic equation
ax² + bx + c = 0
can be solved using the quadratic formula
x = [-b ± √(b² - 4ac)]/2a
Here,
b² - 4ac
is called the discriminant
Let D = b² - 4ac
We want to find the discriminant of the following:
1. 5q² + 2q - 3 = 0
a = 5, b = 2, c = -3
D = 2² - 4(5)(-3)
= 4 + 60
= 64
Discriminant is 64
2. 3u² - 4u + 1 = 0
a = 3, b = -4, c = 1
D = (-4)² - 4(3)(1)
= 16 - 12
= 4
Discriminant is 4
3. 7s² + 9s - 4 = 0
a = 7, b = 9, c = -4
D = 9² - 4(7)(-4)
= 81 + 112
= 193
Discriminant is 193
4. 6w² - 8w + 5 = 0
a = 6, b = -8, c = 5
D = (-8)² - 4(6)(5)
= 64 - 120
= -56
Discriminant is -56
5. 5p² + 7p - 3 = 0
a = 5, b = 7, c = -3
D = 7² - 4(5)(-3)
= 49 + 60
= 109
Discriminant is 109
6. 9f² - 5f + 2 = 0
a = 9, b = -5, c = 2
D = (-5)² - 4(9)(2)
= 25 - 72
= -47
Discriminant is -47
7. 2n² + 6n - 4 = 0
a = 2, b = 6, c = -4
D = 6² - 4(2)(-4)
= 36 + 32
= 68
Discriminant is 68
8. 3d² - 3d + 4 = 0
a = 3, b = -3, c = 4
D = (-3)² - 4(3)(4)
= 9 - 48
= -39
Discriminant is -39
9. 9v² + 4v - 7 = 0
a = 9, b = 4, c = -7
D = 4² - 4(9)(-7)
= 16 + 252
268
Discriminant is 268
10. 4c² + 8c - 5 = 0
a = 4, b = 8, c = -5
D = 8² - 4(4)(-5)
= 64 + 80
= 144
Discriminant is 144.
