Find out the title of his speech by solving the quadratic equations below. Choose the right answer from the table and write the appropriate letter on the corresponding number. C TITLE OF THE SPEECH: I HAVE A E 2 (1, -15) A (2, -6) 1 1. x²9x + 18 = 0
2. 3k²-18k - 21 = 0
3. x² + 14x - 15 = 0 2
4. 5k²= 60 - 20k D 3
5. 4b² +86 +7=4
(3,6) Y (3,6) I (-5, 3) R (7, -1) Pr 4 S 5 (-2,7) M (1/32 312
2. 3k²-18k - 21 = 0
3. x² + 14x - 15 = 0 2
4. 5k²= 60 - 20k D 3
5. 4b² +86 +7=4
(3,6) Y (3,6) I (-5, 3) R (7, -1) Pr 4 S 5 (-2,7) M (1/32 312
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Answer:�
2
+
9
�
+
18
=
0
x
2
+9x+18=0 can be factored as
(
�
+
3
)
(
�
+
6
)
=
0
(x+3)(x+6)=0. So, the solutions are
�
=
−
3
x=−3 and
�
=
−
6
x=−6. None of these solutions match the points (1, -15) or (2, -6).
3
�
2
−
18
�
−
21
=
0
3k
2
−18k−21=0 can be factored as
3
(
�
−
7
)
(
�
+
1
)
=
0
3(k−7)(k+1)=0. So, the solutions are
�
=
7
k=7 and
�
=
−
1
k=−1. None of these solutions match the points (1, -15) or (2, -6).
�
2
+
14
�
−
15
=
0
x
2
+14x−15=0 can be factored as
(
�
+
15
)
(
�
−
1
)
=
0
(x+15)(x−1)=0. So, the solutions are
�
=
−
15
x=−15 and
�
=
1
x=1. None of these solutions match the points (1, -15) or (2, -6).
5
�
2
=
60
−
20
�
5k
2
=60−20k can be rearranged to form
5
�
2
+
20
�
−
60
=
0
5k
2
+20k−60=0. Dividing the equation by 5 gives
�
2
+
4
�
−
12
=
0
k
2
+4k−12=0, which can be factored as
(
�
+
6
)
(
�
−
2
)
=
0
(k+6)(k−2)=0. So, the solutions are
�
=
−
6
k=−6 and
�
=
2
k=2. None of these solutions match the points (1, -15) or (2, -6).
4
�
2
+
86
�
+
7
=
4
4b
2
+86b+7=4 can be rearranged as
4
�
2
+
86
�
+
3
=
0
4b
2
+86b+3=0. Using the quadratic formula, the solutions for
�
b are complex numbers and do not match the given points.
Step-by-step explanation:I think there is an error on your question.
Verified answer
Answer:
To find the title of the speech, let's solve the given quadratic equations and match the results with the options provided in the table.
1. x² + 9x + 18 = 0
Factors: (x + 3)(x + 6) = 0
Roots: x = -3, -6
2. 3k² - 18k - 21 = 0
Factors: (k - 3)(3k + 7) = 0
Roots: k = 3, -7/3
3. x² + 14x - 15 = 0
Factors: (x - 1)(x + 15) = 0
Roots: x = 1, -15
4. 5k² = 60 - 20k
Rearranging: 5k² + 20k - 60 = 0
Factors: (k + 6)(k - 2) = 0
Roots: k = -6, 2
5. 4b² + 86 + 7 = 4
Rearranging: 4b² + 93 = 4
4b² = -89
No real solutions (imaginary solutions)
Matching the roots of the quadratic equations with the options in the table, we have:
1. x² + 9x + 18 = 0 has roots x = -3, -6 (Option C)
2. 3k² - 18k - 21 = 0 has roots k = 3, -7/3 (Option R)
3. x² + 14x - 15 = 0 has roots x = 1, -15 (Option Y)
4. 5k² + 20k - 60 = 0 has roots k = -6, 2 (Option E)
5. The equation 4b² + 93 = 4 has no real solutions (Option N/A for table)
Matching the letters assigned to the options, we can form the title of the speech:
C - R - Y - E - N/A
Therefore, the title of the speech is: "CRY ENA"