Relationship Between Zeros And Coefficients Of A Polynomial Consider 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 = =Product of the zeros = 3 × 5 = 15 = = So if ax2 + bx + c, a ≠ 0 is a quadratic polynomial and α, β are two zeros of polynomial … [Read more...] about Relationship Between Zeros And Coefficients Of A Polynomial

# Polynomials

## Factorization Of Polynomials Using Factor Theorem

Factorization Of Polynomials Using Factor Theorem Factor 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 the Remainder Theorem, p(x) = (x – a) q(x) + p(a). (i) If p(a) = 0, then p(x) = (x – a) q(x), which shows that x – a is a factor of … [Read more...] about Factorization Of Polynomials Using Factor Theorem

## How To Form A Polynomial With The Given Zeroes

Form A Polynomial With The Given Zeros Let 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 zeros)x + Product of the zeros Form A Polynomial With The Given Zeros Example Problems With Solutions Example 1: Form the … [Read more...] about How To Form A Polynomial With The Given Zeroes

## How Do You Determine The Degree Of A Polynomial

Degree Of A Polynomial The 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 of 3x = 1 Since, the greatest power is 7, therefore degree of the polynomial 5x2 – 8x7 + 3x is 7 The degree of polynomial : (i) 4y3 … [Read more...] about How Do You Determine The Degree Of A Polynomial

## Zeros Of A Polynomial Function

Zeros Of A Polynomial Function If 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 the polynomial p(x) = x – 2. (ii) For the polynomial g(u) = u2 – 5u + 6; g(3) = (3)2 – 5 × 3 + 6 = 9 – 15 + 6 = 0 ∴ 3 is a zero of … [Read more...] about Zeros Of A Polynomial Function