Coefficients

Coefficients:

In mathematics, we solve linear equations, quadratic equations and polynomials.

All these are the algebraic equations which includes two or more variables. The variable is the unknown quantity which takes any value.

And the numerical term or value in multiple of the variable is called as coefficient.

Coefficient may be real, imaginary, negative, positive or in decimal also.

For example:

  • ax2 + bx + c = 0

This is the quadratic equation in x which is the variable.

And a is the coefficient of x2.

b is the coefficient of x.

And c is the numerical constant.

 

If any variable is not having any coefficient then its coefficient is always one.

For example:

  • x3 + x2 + 2x + 5 = 0

Here, the coefficient of x3 is 1.

Also the coefficient of x2 is 1 and 2 is the coefficient of x while 5 is the numerical constant.

 

  • If the polynomial is of the form 8x3 -6x2 + 0.5x + 10= 0

In this polynomial, the coefficient of x is 8, coefficient of x2 is -6, coefficient of x is 0.5 and 10 is the numerical constant.

Thus, the coefficients may be positive or negative integers, whole numbers, fractions or decimals.

 

  • There are two types of coefficients one is numerical coefficient and other is the constant coefficient.
  • The numerical coefficients has the fixed numerical value while the constant coefficient has any fixed value which may vary according to the equation.

For example:

  • If the given polynomial is in the form ax3 + 2x2 + bx + 6 = 0

Then, a is the constant coefficient of x3 and which takes any value in order to satisfy the given polynomial.

Also, b is the constant coefficient of x and which takes any value in order to satisfy the given polynomial.

But, 2 is the numerical coefficient of x2, which has fixed numerical value 2.

And 6 is the numerical constant only.


Updated: July 15, 2021 — 11:21 pm

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