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Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3?
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Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x...
Quadratic Equations
Introduction
A quadratic equation is an equation in which the highest power of the variable is 2. It can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
Given Equations
a) x^3 – x = x^2/2
b) √x^4 = x^(1/2)
c) (x+1)(x^2-2) = (x+3)^3
Solution
a) x^3 – x = x^2/2
This is not a quadratic equation because the highest power of x is 3, not 2. Therefore, option a is not a quadratic equation.
b) √x^4 = x^(1/2)
This is not a quadratic equation because there is no variable with a power of 2. Therefore, option b is not a quadratic equation.
c) (x+1)(x^2-2) = (x+3)^3
This is a quadratic equation because the highest power of x is 2. Expanding the brackets, we get:
x^3 - x^2 + x - 2 = x^3 + 9x^2 + 27x + 27
Bringing all the terms to one side, we get:
10x^2 + 26x + 29 = 0
This is a quadratic equation in standard form (ax^2 + bx + c = 0) with a = 10, b = 26, and c = 29. Therefore, option c is a quadratic equation.
Conclusion
Out of the given options, only option c is a quadratic equation. The other options do not have a variable with a power of 2, which is a requirement for a quadratic equation.
Community Answer
Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x...
Ans is option c it is a quadratic equation...
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Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3?
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Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3?.
Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following are quadratic equations a) x 3 –x = x2 2 b) √x 4 = x 1 c) (x 1)(x2 -2) = (x 3)3?.
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