Polynomials - Introduction

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Q1. What is the sum of the roots of the polynomial x^2 + 6x + 9?

Solution:

Step 1: The sum of the roots is given by -b/a: -6/1 = -6.

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Q2. What is the value of x in the equation x^2 - 4 = 0?

Solution:

Step 1: Factor the equation: (x - 2)(x + 2) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Solutions are x = 2 and x = -2.

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Q3. What are the roots of the quadratic equation x^2 - 4 = 0?

Solution:

Step 1: Factor the equation: (x - 2)(x + 2) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Step 3: Roots are x = -2 and x = 2.

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Q4. What is the degree of the polynomial 4x^3 - 2x^2 + x - 5?

Solution:

The degree of a polynomial is the highest power of x. Here, the highest power is 3.

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Q5. What is the result of (3x^2 + 2x) + (4x^2 - 5x)?

Solution:

Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.