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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

Table of content

1. Find the Zeroes of the Polynomial x^2 + ⅙ x – 2 and verify the relation between the Coefficient and Zeroes of the Polynomial

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

Related Questions:-

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

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

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