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Introduction to Linear Polynomials - Linear Polynomials

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A polynomial of degree 11 is called a Linear Polynomial. The degree is the highest power of the variable in the expression.

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The standard form of a linear polynomial in one variable xx is p(x)=ax+bp(x) = ax + b, where aa and bb are real numbers (constants) and a≠0a \neq 0.

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A linear polynomial can have at most two terms. It can be a monomial (e.g., 5x5x) or a binomial (e.g., 5x−35x - 3).

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The value of the variable for which the value of the polynomial becomes zero is called the zero of the polynomial. Every linear polynomial in one variable has exactly one zero.

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If kk is a zero of p(x)=ax+bp(x) = ax + b, then p(k)=ak+b=0p(k) = ak + b = 0.

📐Formulae

p(x)=ax+b, where a≠0p(x) = ax + b, \text{ where } a \neq 0

Zero of p(x)=−Constant termCoefficient of x=−ba\text{Zero of } p(x) = -\frac{\text{Constant term}}{\text{Coefficient of } x} = -\frac{b}{a}

💡Examples

Problem 1:

Find the zero of the linear polynomial p(x)=3x−9p(x) = 3x - 9.

Solution:

3x−9=03x - 9 = 0 3x=93x = 9 x=93x = \frac{9}{3} x=3x = 3

Explanation:

To find the zero of a polynomial, we set the polynomial equal to zero and solve for the variable xx.

Problem 2:

Check whether x=−12x = -\frac{1}{2} is a zero of the polynomial p(x)=2x+1p(x) = 2x + 1.

Solution:

p(−12)=2(−12)+1p\left(-\frac{1}{2}\right) = 2\left(-\frac{1}{2}\right) + 1 p(−12)=−1+1p\left(-\frac{1}{2}\right) = -1 + 1 p(−12)=0p\left(-\frac{1}{2}\right) = 0

Explanation:

Since the value of the polynomial at x=−12x = -\frac{1}{2} is 00, it is confirmed as a zero of the polynomial.

Problem 3:

Identify the linear polynomials from the following list: 5x+35x + 3, x2−4x^2 - 4, 1x+2\frac{1}{x} + 2, 7y7y.

Solution:

The linear polynomials are 5x+35x + 3 and 7y7y.

Explanation:

5x+35x + 3 is a linear polynomial because the highest power of xx is 11. 7y7y is a linear polynomial (monomial) because the power of yy is 11. x2−4x^2 - 4 is a quadratic polynomial (degree 22), and 1x+2\frac{1}{x} + 2 is not a polynomial because the power of xx is −1-1 (not a whole number).