o determine which root is repeated in a cubic equation when you only get two distinct roots, you can use the following method: Steps to Identify the Repeated Root Find the Derivative: Take the derivative of the cubic equation ( f(x) = ax^3 + bx^2 + cx + d ). The derivative is ( f’(x) = 3ax^2 + 2bx + c ). Solve the Derivative: Solve the derivative equation ( f’(x) = 0 ) to find the critical points. These points are potential repeated roots. Check the Original Equation: Substitute the critical points back into the original cubic equation ( f(x) = 0 ). If a critical point satisfies the original equation, it is a repeated root. Example Consider the cubic equation ( f(x) = x^3 - 6x^2 + 11x - 6 ): Find the Derivative: f′(x)=3x2−12x+11 Solve the Derivative: 3x2−12x+11=0 Solving this quadratic equation gives the critical points ( x = 1 ) and ( x = \frac{11}{3} ). Check the Original Equation: Substitute ( x = 1 ) into ( f(x) ):f(1)=13−6(1)2+11(1)−6=0 So, ( x = 1 ) is a root of the original equation and is repeated
o determine which root is repeated in a cubic equation when you only get two distinct roots, you can use the following method: Steps to Identify the Repeated Root Find the Derivative: Take the derivative of the cubic equation ( f(x) = ax^3 + bx^2 + cx + d ). The derivative is ( f’(x) = 3ax^2 + 2bx + c ). Solve the Derivative: Solve the derivative equation ( f’(x) = 0 ) to find the critical points. These points are potential repeated roots. Check the Original Equation: Substitute the critical points back into the original cubic equation ( f(x) = 0 ). If a critical point satisfies the original equation, it is a repeated root. Example Consider the cubic equation ( f(x) = x^3 - 6x^2 + 11x - 6 ): Find the Derivative: f′(x)=3x2−12x+11 Solve the Derivative: 3x2−12x+11=0 Solving this quadratic equation gives the critical points ( x = 1 ) and ( x = \frac{11}{3} ). Check the Original Equation: Substitute ( x = 1 ) into ( f(x) ):f(1)=13−6(1)2+11(1)−6=0 So, ( x = 1 ) is a root of the original equation and is repeated
Press mode again then choose in which you want to go..like if you want complex numbers such as 3+4i should be shown like this and you have mostly calculations based on complex and real numbers both then you should choose "complex " from the setup .to change in complex mode you have to press mode then press 2 or the number which is written before the word " Complex "
o determine which root is repeated in a cubic equation when you only get two distinct roots, you can use the following method:
Steps to Identify the Repeated Root
Find the Derivative:
Take the derivative of the cubic equation ( f(x) = ax^3 + bx^2 + cx + d ). The derivative is ( f’(x) = 3ax^2 + 2bx + c ).
Solve the Derivative:
Solve the derivative equation ( f’(x) = 0 ) to find the critical points. These points are potential repeated roots.
Check the Original Equation:
Substitute the critical points back into the original cubic equation ( f(x) = 0 ). If a critical point satisfies the original equation, it is a repeated root.
Example
Consider the cubic equation ( f(x) = x^3 - 6x^2 + 11x - 6 ):
Find the Derivative:
f′(x)=3x2−12x+11
Solve the Derivative:
3x2−12x+11=0
Solving this quadratic equation gives the critical points ( x = 1 ) and ( x = \frac{11}{3} ).
Check the Original Equation:
Substitute ( x = 1 ) into ( f(x) ):f(1)=13−6(1)2+11(1)−6=0
So, ( x = 1 ) is a root of the original equation and is repeated
A real problem solver video buddy. Keep doing more 🥂
If I get only 2 roots, using the calculator for a cubic equation, how to know which one is repeated?
Yes I have also the same problem
@@rohit028 same problem bro have you got your answer?
The last answer you get is repeating
o determine which root is repeated in a cubic equation when you only get two distinct roots, you can use the following method:
Steps to Identify the Repeated Root
Find the Derivative:
Take the derivative of the cubic equation ( f(x) = ax^3 + bx^2 + cx + d ). The derivative is ( f’(x) = 3ax^2 + 2bx + c ).
Solve the Derivative:
Solve the derivative equation ( f’(x) = 0 ) to find the critical points. These points are potential repeated roots.
Check the Original Equation:
Substitute the critical points back into the original cubic equation ( f(x) = 0 ). If a critical point satisfies the original equation, it is a repeated root.
Example
Consider the cubic equation ( f(x) = x^3 - 6x^2 + 11x - 6 ):
Find the Derivative:
f′(x)=3x2−12x+11
Solve the Derivative:
3x2−12x+11=0
Solving this quadratic equation gives the critical points ( x = 1 ) and ( x = \frac{11}{3} ).
Check the Original Equation:
Substitute ( x = 1 ) into ( f(x) ):f(1)=13−6(1)2+11(1)−6=0
So, ( x = 1 ) is a root of the original equation and is repeated
How would you find the complex number when using fx 100? Please help
But the major problem is how to convert that obtained complex answer into normal decimal form please help....
VIJAYA PRAKASH CHOUHAN s=>D
Yes this is the main problem please can anyone tell
What if you get 2 answers ? How do you get 3rd one ? Plz respond any1
if you get two answers one is likely to be a turning point
Thank you so much ❤️
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Sir how to find upto 4th degree....
Please tell sir very much needed
How to convert it's into the real numbers please reply
Thank u💫
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Thank you Nik!
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how to get back to initial mode from EQN mode? Which number to press?
Press mode again then choose in which you want to go..like if you want complex numbers such as 3+4i should be shown like this and you have mostly calculations based on complex and real numbers both then you should choose "complex " from the setup .to change in complex mode you have to press mode then press 2 or the number which is written before the word " Complex "
Thanks a lot, 😍
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Where cubic roots bro we need in single number not in decimals
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Thanks man
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U the boooooooss 😎
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Cube root please tell this
Thank you
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Thank you so much
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Thank u
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Thank you bro
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Welcome