Polynomial in Hindi, deals with various concepts which are as under:-
- Polynomial (बहुपद )
- Coefficient ( गुणांक )
- Degree of the Polynomial
- Zero Polynomial (शून्य बहुपद )
- Constant Polynomial (अचर बहुपद )
- Linear Polynomial (रैखिक बहुपद)
- Quadratic Polynomial (द्विघात बहुपद)
- Cubic Polynomial (त्रघाती बहुपद)
- BI-Quadratic Polynomial
- Value of a Polynomial (बहुपद का मान )
- Zero of the Polynomial (बहुपद के शून्यंक)
- Degree of a Polynomial Example
Polynomial (बहुपद )
A polynomial is an algebraic expression of the form p(x) = an xn + an-1 xn-1 +……..+ a1 x1 + a0, where an, an-1, a1, a0 are real numbers and an≠ 0 is called a polynomial.
where an xn , an-1 xn-1 +…….., a1 x1 , a0, are the terms of a polynomial and an , an-1 ,…….., a1, a0 are their coefficients.
Coefficient ( गुणांक )
The real number that precedes the variable is called the coefficient.
A polynomial involving one variable is called a polynomial in one variable.
Degree of the Polynomial
The exponent of the highest power of the variable of a polynomial is called the degree of the polynomial.
Based on its degree, a polynomial can be called as linear polynomial, quadratic polynomial, cubic polynomial and so on.
Zero Polynomial (शून्य बहुपद )
The polynomial with all the coefficients as zeros is called a zero polynomial.
Constant Polynomial (अचर बहुपद )
A polynomial with a single term of a real number is called a constant polynomial.
Linear Polynomial (रैखिक बहुपद)
A polynomial of degree one is called a first-degree or linear polynomial. The general form of a linear polynomial is ax + b, where a and b are real numbers and a ≠ 0.
Quadratic Polynomial (द्विघात बहुपद)
A polynomial of degree two is called a second degree or quadratic polynomial. The general form of a quadratic polynomial is ax2 + bx + c, where a,b and c are real numbers and a ≠ 0.
Cubic Polynomial (त्रघाती बहुपद)
A polynomial of degree three is called a third-degree or cubic polynomial. The general form of a cubic polynomial is ax3 + bx2 + cx + d, where a,b,c and d are real numbers and a ≠ 0.
BI-Quadratic Polynomial
A polynomial of degree four is called a fourth-degree or biquadratic polynomial. The general form of a quadratic polynomial is ax4 + bx3 + cx2 + dx + e, where a,b,c,d and e are real numbers and a ≠ 0.
Value of a Polynomial (बहुपद का मान )
The value of a polynomial p(x) when x = k (k is a real number) is the value obtained by substituting x as k. It is denoted by p(k).
Zero of the Polynomial (बहुपद के शून्यंक)
The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.
Degree of a Polynomial Example
Find the Degree of the Polynomials?
निम्न बहुपदों की घात पता कीजिए?
In this polynomial the highest power of the variable is 7 so the degree of the polynomial will be 7.
In this polynomial the highest power of the variable y is 6 so the degree of the polynomial will be 7.
C) 15
In this there are no variable so the degree will be 0. The polynomial with degree 0 is called as constant.