Question

write the relation between the zeros and the coefficient of polynomial​

Answer 1

Step-by-step explanation:

if a is zero of a polynomial p(x) then (x – a) is a factor of p(x). The general form of linear polynomial is p(x) = ax+b, its zero is -ba -b a . i.e.x = -ba -b a or - Constant term Coefficient of x - Constant term Coefficient of x , General form of quadratic polynomial is ax 2 + bx +c where a ≠ 0.

Answer 2

Answer:

Relationship Between the Zeros and Coefficients of a Polynomial

A real number say “a” is a zero of a polynomial P(x) if P(a) = 0. The zero of a polynomial is clearly explained using the Factor theorem. If “k” is a zero of a polynomial P(x), then (x-k) is a factor of a given polynomial. The relation between the zeros and the coefficients of a polynomial is given below:

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

Zeros of a Polynomial Solved Examples

Example:

Evaluate the sum and product of zeros of the quadratic polynomial 4x2 – 9.

Solution:

Given quadratic polynomial is 4x2 – 9.

4x2 – 9 can be written as 2x2 – 33, which is equal to (2x+3)(2x-3).

To find the zeros of a polynomial, equate the above expression to 0

(2x+3)(2x-3) = 0

2x+3 = 0

2x = -3

X = -3/2

Similarly, 2x-3 = 0,

2x = 3

x = 3/2

Therefore, the zeros of a given quadratic polynomial is 3/2 and -3/2.

Finding the sum and product of a polynomial:

The sum of the zeros = (3/2)+ (-3/2) = (3/2)-(3/2) = 0

The product of zeros = (3/2).(-3/2) = -9/4.