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2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.?
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2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.?
Explanation of the Roots of the Cubic Equation x3 - 2x2 - x - 2 = 0
- Introduction: The given cubic equation is x3 - 2x2 - x - 2 = 0.
- Finding the Roots: To find the roots of the cubic equation, we can use different methods such as factoring, synthetic division, or the rational root theorem. However, in this case, none of these methods work, so we use the Cardano's formula to find the roots.
- Cardano's Formula: The Cardano's formula is a method to find the roots of a cubic equation. It is given as follows:
- Applying Cardano's Formula: To apply Cardano's formula to the given cubic equation, we need to transform it into the standard form:
- Transforming the Equation: We can transform the given equation into the standard form as follows:
- Roots of the Equation: The roots of the cubic equation x3 - 2x2 - x - 2 = 0 are:
- Conclusion: Therefore, the given cubic equation has 3 roots, which are x = 2, x = 1, and x = -2.
x = [(q + (q2 + 4r3)1/2)/2]1/3 + [(q - (q2 + 4r3)1/2)/2]1/3
x3 + px + q = 0
x3 - 2x2 - x - 2 = 0
x3 - 2x2 + x - 3x - 2 = 0
x2(x - 2) + (x - 2)(x + 1) = 0
(x - 2)(x2 + x - 2) = 0
(x - 2)(x - 1)(x + 2) = 0
x = 2, x = 1, x = -2
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2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.?
X³+2X²-X-2=0
X³+X²+X²+X-2X-2=0
X²(X+1)+X(X+1)-2(X+1)=0
(X+1) (X²+x-2)=0
X+1=0 and X²+X-2=0
X²+X-2=0
X²+2X-X-2=0
X(X+2)-1(X+2)=0
(X+2) (X-1) =0
X+2=0 , X-1=0
X= -2, X= 1 and X = -1
X³+X²+X²+X-2X-2=0
X²(X+1)+X(X+1)-2(X+1)=0
(X+1) (X²+x-2)=0
X+1=0 and X²+X-2=0
X²+X-2=0
X²+2X-X-2=0
X(X+2)-1(X+2)=0
(X+2) (X-1) =0
X+2=0 , X-1=0
X= -2, X= 1 and X = -1
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2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.?.
2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2. The cubic equation x3 2x2-x-2 = 0 has 3 roots namely.?.
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