Polynomials

Relationship Between Zeros And Coefficients Of A PolynomialConsider quadratic polynomial P(x) = 2x2 – 16x + 30. Now, 2x2 – 16x + 30 = (2x – 6) (x – 3) = 2 (x – 3) (x – 5) The zeros of P(x) are 3 and 5. Sum of the zeros = 3 + 5 = 8 = (frac {…

Factorization Of Polynomials Using Factor TheoremFactor Theorem:If p(x) is a polynomial of degree n  1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). Proof: By…

Factorization Of Polynomials Using Factor TheoremFactor Theorem:If p(x) is a polynomial of degree n  1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). Proof: By…

Form A Polynomial With The Given ZerosLet zeros of a quadratic polynomial be α and β. x = β,               x = β x – α = 0,   x ­– β = 0 The obviously the quadratic polynomial is (x – α) (x – β) i.e.,  x2 – (α + β) x + αβ x2 – (Sum of the…

Degree Of A PolynomialThe greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : In polynomial 5x2 – 8x7 + 3x: (i) The power of term 5x2 = 2 (ii) The power of term –8x7 = 7 (iii) The power…

Degree Of A PolynomialThe greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : In polynomial 5x2 – 8x7 + 3x: (i) The power of term 5x2 = 2 (ii) The power of term –8x7 = 7 (iii) The power…

Zeros Of A Polynomial FunctionIf for x = a, the value of the polynomial p(x) is 0 i.e., p(a) = 0; then x = a is a zero of the polynomial p(x).For Example: (i) For polynomial p(x) = x – 2; p(2) = 2 – 2 = 0 ∴ x = 2 or simply 2 is a zero of…

Types Of Polynomials(i) Based on degree : If degree of polynomial isExamples1.One  Linearx + 3, y – x + 2, √3x –32.TwoQuadratic2x2 –7, (frac{1}{3}^{2}}+^{2}}-2text{xy}), x2 +1+ 3y3.ThreeCubicx3 + 3x2 –7x+8, 2x2+5x3+7,4.Fourbi-quadraticx4 +…

Types Of Polynomials(i) Based on degree : If degree of polynomial isExamples1.One  Linearx + 3, y – x + 2, √3x –32.TwoQuadratic2x2 –7, (frac{1}{3}^{2}}+^{2}}-2text{xy}), x2 +1+ 3y3.ThreeCubicx3 + 3x2 –7x+8, 2x2+5x3+7,4.Fourbi-quadraticx4 +…

Factorise A Polynomial By Splitting The Middle Term Example Problems With SolutionsType I: Factorization of Quadratic polynomials of the form x2 + bx + c. (i) In order to factorize x2 + bx + c we have to find numbers p and q such that p + q…