Find the Zeroes of the Polynomial x2 + ⅙ x - 2 and verify the relation between the coefficient and zeroes of the polynomial

By K Balaji|Updated : November 13th, 2022

The zeroes of the polynomial x2 + ⅙ x - 2 are 4/3 and -3/2.

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Step 1: Form the equation

The given polynomial is x2 + ⅙ x - 2

We are aware that a polynomial's zeroes are evaluated by equating it to zero.

p(x) = 0

x2 + ⅙ x - 2 = 0

Step 2: Solve to find the zeroes

x2 + ⅙ x - 2 = 0

Multiplying by 6

6x2 + x - 12 = 0

The above equation can be written as

6x2 - 8x + 9x - 12 = 0

Taking common we get

2x (3x - 4) + 3 (x - 4) = 0

(3x - 4) (2x + 3) = 0

x = 4/3, -3.2

Step 3: Check the relationship between the coefficients.

Let the zeros of the given polynomial be a and b.

where a = 4/3, b = -3/2

A polynomial can also be written as,

x2 - (a + b)x + ab = 0

Substituting the values we get

x2 - (4/3 - 3/2)x + {4/3 x (-3/2)} = 0

x2 - (8 - 9)/6 x + (-2) = 0

x2 + ⅙ x - 2 = 0

The relationship between the polynomial's coefficient and zeroes has been confirmed because this is the original supplied polynomial.

As a result, this polynomial's zeros are 4/3 and -3/2.

Summary:-

Find the Zeroes of the Polynomial x^2 + ⅙ x - 2 and verify the relation between the Coefficient and Zeroes of the Polynomial

The zeroes of the polynomial x2 + ⅙ x - 2 are 4/3 and -3/2. A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

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