To solve the problem, we need to determine the degree of the quadratic equation \( ax^2 + bx + c = 0 \), where \( a \neq 0 \).
1. Understanding the Degree of an Equation:
The degree of a polynomial equation is defined as the highest power of the variable (in this case, \( x \)) with a non-zero coefficient.
2. Analyzing the Given Equation:
The given equation is:
\( ax^2 + bx + c = 0 \)
Here, the term with the highest exponent is \( ax^2 \), and since \( a \neq 0 \), this term exists.
3. Identifying the Degree:
The exponent of \( x \) in the leading term \( ax^2 \) is 2. Hence, the degree of the equation is 2.
Final Answer:
The degree of the quadratic equation is 2.
Match List I with List II :
| List I (Quadratic equations) | List II (Roots) |
|---|---|
| (A) \(12x^2 - 7x + 1 = 0\) | (I) \((-13, -4)\) |
| (B) \(20x^2 - 9x + 1 = 0\) | (II) \(\left(\frac{1}{3}, \frac{1}{4}\right)\) |
| (C) \(x^2 + 17x + 52 = 0\) | (III) \((-4, -\frac{3}{2})\) |
| (D) \(2x^2 + 11x + 12 = 0\) | (IV) \(\left(\frac{1}{5}, \frac{1}{4}\right)\) |
Choose the correct answer from the options given below :