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The roots of the cubic equation x3 + 7x2 - 21x - 27 = 0
- a)-1,3,9
- b)1,-3,9
- c)-1,3,-9
- d)-1,-3,9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The roots of the cubic equation x3+ 7x2- 21x - 27 = 0a)-1,3,9b)1,-3,9c...
Solution:
Given cubic equation is x3 7x2- 21x - 27 = 0
To find: The roots of the given cubic equation
Method:
To find the roots of the given cubic equation, we will use the factor theorem which states that if a polynomial f(x) is divided by (x-a), then the remainder will be zero if and only if (x-a) is a factor of f(x).
Steps:
1. First, we will check whether any of the given options satisfies the given cubic equation by substituting the values of x from the options.
2. On substituting the value of x in the given cubic equation, we will check whether the left-hand side (LHS) of the equation is equal to zero or not.
3. If the LHS of the equation is zero, then the substituted value is a root of the given cubic equation.
Calculation:
On substituting the value of x = -1 in the given cubic equation, we get
(-1)3 + 7(-1)2 - 21(-1) - 27 = -1 - 7 + 21 - 27 = -14
Therefore, x = -1 is not a root of the given cubic equation.
On substituting the value of x = 3 in the given cubic equation, we get
3^3 + 7(3)2 - 21(3) - 27 = 27 + 63 - 63 - 27 = 0
Therefore, x = 3 is a root of the given cubic equation.
On substituting the value of x = -9 in the given cubic equation, we get
(-9)3 + 7(-9)2 - 21(-9) - 27 = -729 + 567 + 189 - 27 = 0
Therefore, x = -9 is a root of the given cubic equation.
Therefore, the roots of the given cubic equation are -1, 3, and -9.
Answer:
Option (C) -1, 3, -9 is the correct answer.
Given cubic equation is x3 7x2- 21x - 27 = 0
To find: The roots of the given cubic equation
Method:
To find the roots of the given cubic equation, we will use the factor theorem which states that if a polynomial f(x) is divided by (x-a), then the remainder will be zero if and only if (x-a) is a factor of f(x).
Steps:
1. First, we will check whether any of the given options satisfies the given cubic equation by substituting the values of x from the options.
2. On substituting the value of x in the given cubic equation, we will check whether the left-hand side (LHS) of the equation is equal to zero or not.
3. If the LHS of the equation is zero, then the substituted value is a root of the given cubic equation.
Calculation:
On substituting the value of x = -1 in the given cubic equation, we get
(-1)3 + 7(-1)2 - 21(-1) - 27 = -1 - 7 + 21 - 27 = -14
Therefore, x = -1 is not a root of the given cubic equation.
On substituting the value of x = 3 in the given cubic equation, we get
3^3 + 7(3)2 - 21(3) - 27 = 27 + 63 - 63 - 27 = 0
Therefore, x = 3 is a root of the given cubic equation.
On substituting the value of x = -9 in the given cubic equation, we get
(-9)3 + 7(-9)2 - 21(-9) - 27 = -729 + 567 + 189 - 27 = 0
Therefore, x = -9 is a root of the given cubic equation.
Therefore, the roots of the given cubic equation are -1, 3, and -9.
Answer:
Option (C) -1, 3, -9 is the correct answer.
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Community Answer
The roots of the cubic equation x3+ 7x2- 21x - 27 = 0a)-1,3,9b)1,-3,9c...
Roots of cubic equation=a,b,y
sum of roots(a+B+y)=-B/A
multiply of roots= -D/A
then use gbc
C option
sum of roots=-1+3-9=-7
multiply of roots= -1×3×(-9)=27
sum of roots(a+B+y)=-B/A
multiply of roots= -D/A
then use gbc
C option
sum of roots=-1+3-9=-7
multiply of roots= -1×3×(-9)=27
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The roots of the cubic equation x3+ 7x2- 21x - 27 = 0a)-1,3,9b)1,-3,9c)-1,3,-9d)-1,-3,9Correct answer is option 'C'. Can you explain this answer?
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