Find the zeroes of the polynomial : p(x) = (x - 2)² - (x + 2)²

Solution:

Given, the polynomial is p(x) = (x - 2)² - (x + 2)²

We have to find the zeros of the polynomial.

For some values of the variable the polynomial will be equal to zero. These values are called zeros of polynomial.

To find zeros of polynomial,

Let p(x) = 0

(x - 2)² - (x + 2)² = 0

Using algebraic identity,

(a - b)² = a² - 2ab + b²

(x - 2)² = x² - 4x + 4

Using algebraic identity,

(a + b)² = a² + 2ab + b²

(x + 2)² = x² + 4x + 4

So, x² - 4x + 4 - (x² + 4x + 4) = 0

x² - 4x + 4 - x² - 4x - 4 = 0

x² - x² - 4x - 4x + 4 - 4 = 0

-4x - 4x = 0

-8x = 0

x = 0

Therefore, the zeros of the polynomial is 0.

✦ Try This: Find the zeroes of the polynomial : p(x) = (x - 2)² - (x - 3)² - 8

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 12

Find the zeroes of the polynomial : p(x) = (x - 2)² - (x + 2)²

Summary:

The standard form of a polynomial refers to writing a polynomial in the descending power of the variable. The zeroes of the polynomial p(x) = (x - 2)² - (x + 2)² is 0

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☛ Related Questions:

• By actual division, find the quotient and the remainder when the first polynomial is divided by the . . . .
• By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ - 2x² - 4x - . . . .
• By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ - 3x² + 4x + . . . .