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Which of the following is not an example of polynomial function ?
- a)g(x) = 8x2 + 5x – 2
- b)p(x) =5x3 + 3x2 + x – 2
- c)h(x) =3 root of x minus 1 over x
- d)f(x) = 3x2 + x – 2
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is not an example of polynomial function ?a)g(x...
A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation.
In option C, powers of x are negative and fractional.
In option C, powers of x are negative and fractional.
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Which of the following is not an example of polynomial function ?a)g(x...
G(x) = divisor p(x) = divident f(x) = polynomial h(x) is nothing in whole algebra chapter it is same as real no. class 10 ch 1 formula and in algebra it is p(x) =g(x)× q(x)+r(x) called algebra algorithm.
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Which of the following is not an example of polynomial function ?a)g(x...
Understanding Polynomial Functions
A polynomial function is defined as a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is:
- f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0
where n is a non-negative integer, and a_n, a_(n-1), ..., a_0 are constants.
Identifying the Functions
Let's analyze the given options to determine which one is not a polynomial:
- a) g(x) = 8x^2 + 5x - 2
- This is a polynomial of degree 2 (the highest exponent is 2).
- b) p(x) = 5x^3 + 3x^2 + x - 2
- This is a polynomial of degree 3 (the highest exponent is 3).
- c) h(x) = (x - 1)/x
- This expression involves division by x. It can be rewritten as h(x) = 1 - (1/x), which contains a term with a negative exponent (-1). Thus, it is not a polynomial because polynomial functions cannot have variables in the denominator or negative exponents.
- d) f(x) = 3x^2 + x - 2
- This is a polynomial of degree 2 (the highest exponent is 2).
Conclusion
Hence, option c is the correct answer because it does not meet the criteria of polynomial functions due to the presence of a term with a negative exponent.
A polynomial function is defined as a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is:
- f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0
where n is a non-negative integer, and a_n, a_(n-1), ..., a_0 are constants.
Identifying the Functions
Let's analyze the given options to determine which one is not a polynomial:
- a) g(x) = 8x^2 + 5x - 2
- This is a polynomial of degree 2 (the highest exponent is 2).
- b) p(x) = 5x^3 + 3x^2 + x - 2
- This is a polynomial of degree 3 (the highest exponent is 3).
- c) h(x) = (x - 1)/x
- This expression involves division by x. It can be rewritten as h(x) = 1 - (1/x), which contains a term with a negative exponent (-1). Thus, it is not a polynomial because polynomial functions cannot have variables in the denominator or negative exponents.
- d) f(x) = 3x^2 + x - 2
- This is a polynomial of degree 2 (the highest exponent is 2).
Conclusion
Hence, option c is the correct answer because it does not meet the criteria of polynomial functions due to the presence of a term with a negative exponent.
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Which of the following is not an example of polynomial function ?a)g(x) = 8x2+ 5x – 2b)p(x) =5x3+ 3x2+ x – 2c)h(x) =3 root of x minus 1 over xd)f(x) = 3x2+ x – 2Correct answer is option 'C'. Can you explain this answer?
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