What value of C will provide coincidental roots in the equation $x^3 + 8x^2 + 9x + (18+c)$? [closed]
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What value of C will provide two coincidental roots in the equation $x^3 + 8x^2 + 9x + (18+c)$?
cubic-equations
asked Nov 16 at 0:42
Mr. Janssens
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closed as off-topic by amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs Nov 16 at 23:41
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What value of C will provide two coincidental roots in the equation $x^3 + 8x^2 + 9x + (18+c)$?
cubic-equations
asked Nov 16 at 0:42
Mr. Janssens
11
closed as off-topic by amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs Nov 16 at 23:41
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What value of C will provide two coincidental roots in the equation $x^3 + 8x^2 + 9x + (18+c)$?
cubic-equations
asked Nov 16 at 0:42
Mr. Janssens
11
What value of C will provide two coincidental roots in the equation $x^3 + 8x^2 + 9x + (18+c)$?
cubic-equations
cubic-equations
asked Nov 16 at 0:42
Mr. Janssens
11
asked Nov 16 at 0:42
Mr. Janssens
11
asked Nov 16 at 0:42
Mr. Janssens
11
asked Nov 16 at 0:42
Mr. Janssens
11
asked Nov 16 at 0:42
Mr. Janssens
11
11
closed as off-topic by amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs Nov 16 at 23:41
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs Nov 16 at 23:41
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Paul Frost, Trevor Gunn, Scientifica, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
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2 Answers
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It means that the equation is of the form: $$(x-a)^2(x-b)=x^3-(2a+b)x^2+(a^2+2ab)x-a^2b = x^3 + 8x^2 + 9x + (18+c)$$
Therefore:
$$begin{cases}2a+b=-8 \ a^2+2ab=9 \ a^2 b=-(18+c)end{cases} $$
Solve for $c$.
answered Nov 16 at 0:59
I like Serena
3,1981718
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Do you know about the cubic discriminant? It is a function of the four coefficients, and there is a repeated root if and only if the cubic discriminant is $0$. In this case, solve $$8^29^2-4cdot9^3-4cdot8^3(18+c)-27(18+c)^2+18cdot8cdot9(18+c)=0$$
There are other approaches where you would not need to know/look up the cubic disciminant.
answered Nov 16 at 0:51
alex.jordan
37.9k559118
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
It means that the equation is of the form: $$(x-a)^2(x-b)=x^3-(2a+b)x^2+(a^2+2ab)x-a^2b = x^3 + 8x^2 + 9x + (18+c)$$
Therefore:
$$begin{cases}2a+b=-8 \ a^2+2ab=9 \ a^2 b=-(18+c)end{cases} $$
Solve for $c$.
answered Nov 16 at 0:59
I like Serena
3,1981718
add a comment |
up vote
2
down vote
It means that the equation is of the form: $$(x-a)^2(x-b)=x^3-(2a+b)x^2+(a^2+2ab)x-a^2b = x^3 + 8x^2 + 9x + (18+c)$$
Therefore:
$$begin{cases}2a+b=-8 \ a^2+2ab=9 \ a^2 b=-(18+c)end{cases} $$
Solve for $c$.
answered Nov 16 at 0:59
I like Serena
3,1981718
add a comment |
up vote
2
down vote
up vote
2
down vote
It means that the equation is of the form: $$(x-a)^2(x-b)=x^3-(2a+b)x^2+(a^2+2ab)x-a^2b = x^3 + 8x^2 + 9x + (18+c)$$
Therefore:
$$begin{cases}2a+b=-8 \ a^2+2ab=9 \ a^2 b=-(18+c)end{cases} $$
Solve for $c$.
answered Nov 16 at 0:59
I like Serena
3,1981718
It means that the equation is of the form: $$(x-a)^2(x-b)=x^3-(2a+b)x^2+(a^2+2ab)x-a^2b = x^3 + 8x^2 + 9x + (18+c)$$
Therefore:
$$begin{cases}2a+b=-8 \ a^2+2ab=9 \ a^2 b=-(18+c)end{cases} $$
Solve for $c$.
answered Nov 16 at 0:59
I like Serena
3,1981718
answered Nov 16 at 0:59
I like Serena
3,1981718
answered Nov 16 at 0:59
I like Serena
3,1981718
answered Nov 16 at 0:59
I like Serena
3,1981718
3,1981718
add a comment |
add a comment |
up vote
1
down vote
Do you know about the cubic discriminant? It is a function of the four coefficients, and there is a repeated root if and only if the cubic discriminant is $0$. In this case, solve $$8^29^2-4cdot9^3-4cdot8^3(18+c)-27(18+c)^2+18cdot8cdot9(18+c)=0$$
There are other approaches where you would not need to know/look up the cubic disciminant.
answered Nov 16 at 0:51
alex.jordan
37.9k559118
add a comment |
up vote
1
down vote
Do you know about the cubic discriminant? It is a function of the four coefficients, and there is a repeated root if and only if the cubic discriminant is $0$. In this case, solve $$8^29^2-4cdot9^3-4cdot8^3(18+c)-27(18+c)^2+18cdot8cdot9(18+c)=0$$
There are other approaches where you would not need to know/look up the cubic disciminant.
answered Nov 16 at 0:51
alex.jordan
37.9k559118
add a comment |
up vote
1
down vote
up vote
1
down vote
Do you know about the cubic discriminant? It is a function of the four coefficients, and there is a repeated root if and only if the cubic discriminant is $0$. In this case, solve $$8^29^2-4cdot9^3-4cdot8^3(18+c)-27(18+c)^2+18cdot8cdot9(18+c)=0$$
There are other approaches where you would not need to know/look up the cubic disciminant.
answered Nov 16 at 0:51
alex.jordan
37.9k559118
Do you know about the cubic discriminant? It is a function of the four coefficients, and there is a repeated root if and only if the cubic discriminant is $0$. In this case, solve $$8^29^2-4cdot9^3-4cdot8^3(18+c)-27(18+c)^2+18cdot8cdot9(18+c)=0$$
There are other approaches where you would not need to know/look up the cubic disciminant.
answered Nov 16 at 0:51
alex.jordan
37.9k559118
answered Nov 16 at 0:51
alex.jordan
37.9k559118
answered Nov 16 at 0:51
alex.jordan
37.9k559118
answered Nov 16 at 0:51
alex.jordan
37.9k559118
37.9k559118
add a comment |
add a comment |
