Identify the quadratic equation: Which of the following is a quadratic equation (an equation of degree 2)?

Introduction / Context:A quadratic equation is any equation that can be written in the standard form ax^2 + bx + c = 0 with a ≠ 0. We examine each option for its degree after arranging it as an equation (if needed) to decide which one is quadratic.

Given Data / Assumptions:

• Degree means the highest power of x in the equation after simplification.
• We can rearrange expressions like “x^4 − 10” to an equation by setting them equal to zero if intended.

Concept / Approach:Check each option’s degree. Quadratic ⇔ degree 2 once terms are brought to one side. Anything of degree 3, 4, or higher (or not an equation) is not quadratic.

Step-by-Step Solution:

Verification / Alternative check:Solving (c) gives x^2 = 7 ⇒ real solutions x = ±√7, consistent with a quadratic form.

Why Other Options Are Wrong:

• (a), (d), (e): Not degree 2; they are cubic, quartic, and quintic respectively.
• (b): Also degree 4 when written as x^4 − 10 = 0.

Common Pitfalls:Confusing “contains x^2” with “is quadratic.” Presence of higher powers (x^3, x^4, etc.) means the equation is not quadratic.

Final Answer:7x^2 = 49