A polynomial is an algebraic expression consisting of variables and coefficients combined using addition subtraction and multiplication. It includes terms with non-negative integer exponents. Polynomials are used to represent various mathematical relationships and solve problems in geometry physics and engineering. Their degree determines the highest power of the variable. Understanding polynomials is essential for advanced mathematics.
Class 10 Maths Chapter 2 Polynomials explores the relationship between zeros and coefficients of polynomials and the division algorithm. It includes linear quadratic and cubic polynomials. This chapter enhances problem-solving skills and prepares students for CBSE Exam 2024-25. Understanding these concepts is crucial for mastering algebra and solving real-life problems. A strong grasp of polynomials ensures a solid foundation for advanced mathematics and improves logical reasoning abilities.
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Solving for the Unknown Zero of a Quadratic Polynomial
Step 1: Given Information
– Polynomial: 2x² + 7x + 3
– One known zero: -3/2
Step 2: Vieta’s Formulas for Quadratic Polynomials
Let the two zeros be p and q:
– p + q = -b/a
– p * q = c/a
Where in 2x² + 7x + 3:
– a = 2
– b = 7
– c = 3
Step 3: Using the Known Zero
If p = -3/2, then we need to find q
Sum of zeros formula:
p + q = -b/a
-3/2 + q = -7/2
Step 4: Solving for the Unknown Zero
q = -7/2 – (-3/2)
= -7/2 + 3/2
= -4/2
= -2
Verification:
– First zero: p = -3/2
– Second zero: q = -2
– Check: (-3/2) + (-2) = -7/2 ✓
– Check: (-3/2) * (-2) = 3/a ✓
Mathematical Insight:
Vieta’s formulas provide a powerful method to find
polynomial zeros without fully solving the equation.
Conclusion:
The other zero of the polynomial is -2 (or 1 in the given options).
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