To check if 3, 4, and 5 are zeroes of the cubic polynomial p(x) = x³ - 12x² + 47x - 60, we can substitute these values into the polynomial and see if the result is equal to zero.
Step-by-step explanation:
1. Substitute x = 3 into p(x):
p(3) = (3)³ - 12(3)² + 47(3) - 60
= 27 - 108 + 141 - 60
= 0
Since the result is zero, 3 is a zero of the polynomial.
2. Substitute x = 4 into p(x):
p(4) = (4)³ - 12(4)² + 47(4) - 60
= 64 - 192 + 188 - 60
= 0
Similarly, the result is zero, indicating that 4 is a zero of the polynomial.
3. Substitute x = 5 into p(x):
p(5) = (5)³ - 12(5)² + 47(5) - 60
= 125 - 300 + 235 - 60
= 0
Once again, the result is zero, confirming that 5 is a zero of the polynomial.
Therefore, based on the calculations, we can conclude that 3, 4, and 5 are zeroes of the cubic polynomial p(x) = x³ - 12x² + 47x - 60.
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Answers & Comments
Verified answer
[tex] = {x}^{3} - 12 {x}^{2} + 47x - 60 \\ \\ = ( {3)}^{3} - 12( {3)}^{2} + 47(3) \\ - 60 \\ \\ = 27 - 12(9) + 141 - 60 \\ \\ = 27 - 108 + 81 \\ \\ = - 81 + 81 \\ \\ = 0[/tex]
[tex]= {x}^{3} - 12 {x}^{2} + 47x - 60 \\ \\ = {(4)}^{3} - 12( {4)}^{2} + 47(4) \\ - 60 \\ \\ = 64 - 12(16) + 188 - 60 \\ \\ = 64 - 192 + 188 - 60 \\ \\ = - 128 + 128 \\ \\ = 0[/tex]
[tex]= {x}^{3} - 12 {x}^{2} + 47x - 60 \\ \\ = ( {5)}^{3} - 12( {5)}^{2} + 47(5) \\ - 60 \\ \\ = 125 - 12(25) + 235 - 60 \\ \\ = 125 - 300 + 175 \\ \\ = - 175 + 175 \\ \\ = 0[/tex]
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Answer:
To check if 3, 4, and 5 are zeroes of the cubic polynomial p(x) = x³ - 12x² + 47x - 60, we can substitute these values into the polynomial and see if the result is equal to zero.
Step-by-step explanation:
1. Substitute x = 3 into p(x):
p(3) = (3)³ - 12(3)² + 47(3) - 60
= 27 - 108 + 141 - 60
= 0
Since the result is zero, 3 is a zero of the polynomial.
2. Substitute x = 4 into p(x):
p(4) = (4)³ - 12(4)² + 47(4) - 60
= 64 - 192 + 188 - 60
= 0
Similarly, the result is zero, indicating that 4 is a zero of the polynomial.
3. Substitute x = 5 into p(x):
p(5) = (5)³ - 12(5)² + 47(5) - 60
= 125 - 300 + 235 - 60
= 0
Once again, the result is zero, confirming that 5 is a zero of the polynomial.
Therefore, based on the calculations, we can conclude that 3, 4, and 5 are zeroes of the cubic polynomial p(x) = x³ - 12x² + 47x - 60.
I hope this helps!
Please mark me as brainiest, give thanks for my answer and rate a good rating because it really helps me out.
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