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Chapter 2 Polynomials

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  Chapter 2 Polynomials A polynomial is an expression consists of constants, variables and exponents. It’s mathematical form is- a­­­ n x n  + a n-1 x n-1  + a n-2 x n-2  + a 2 x 2  + a 1 x + a 0  = 0 where the (a i )’s are constant Degree of Polynomials Let P(y) is a polynomial in y, then the highest #ffffcc power of y in the P(y) will be the degree of polynomial P(y). Types of Polynomial according to their Degrees Type of polynomial Degree Form Constant 0 P(x) = a Linear 1 P(x) = ax + b Quadratic 2 P(x) = ax 2  + ax + b Cubic 3 P(x) = ax 3  + ax 2  + ax + b Bi-quadratic 4 P(x) = ax 4  + ax 3  + ax 2  + ax + b Value of Polynomial Let p(y) is a polynomial in y and α could be any real number, then the value calculated after putting the value y = α in p(y) is the final value of p(y) at y = α. This shows that p(y) at y = α is represented by p (α). Zero of a Polynomial If the value of p(y) at y = k is 0, that is p (k) = 0 then y = ...
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QUADRATIC EQUATIONS

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Quadratic Polynomial A polynomial, whose degree is 2, is called a quadratic polynomial. It is in the form of p(x) = ax 2  + bx + c,  where a ≠ 0 Quadratic Equation When we equate the quadratic polynomial to zero then it is called a Quadratic Equation i.e. if p(x) = 0 , then it is known as Quadratic Equation.  Standard form of Quadratic Equation where a, b, c are the real numbers and a≠0 Types of Quadratic Equations 1. Complete Quadratic Equation   ax 2  + bx + c = 0, where a ≠ 0, b ≠ 0, c ≠ 0 2. Pure Quadratic Equation    ax 2  = 0, where a ≠ 0, b = 0, c = 0 Roots of a Quadratic Equation Let x = α where α is a real number. If α satisfies the Quadratic Equation ax 2 + bx + c = 0 such that aα 2  + bα + c = 0, then  α is the root of the Quadratic Equation . As quadratic polynomials have degree 2, therefore Quadratic Equations can have two roots. So the zeros of quadratic polynomial p(x) =ax 2 +bx+c is same as the roots of the Quadratic Equa...
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