Question

Out of the following equations, which one is not a quadratic equation?

• A. \(x^2 + 4x = 11 + x^2\)
• B. \(x^2 = 4x\)
• C. \(5x^2 = 90\)
• D. \(2x - x^2 = x^2 + 5\)

Hint:

To check whether an equation is quadratic, rearrange it in standard form \(ax^2 + bx + c = 0\). If the \(x^2\) term cancels out, the equation is not quadratic.

Answer 1

The Correct Option is A

Step 1: Recall the definition of a quadratic equation.
A quadratic equation is an equation of the form \(ax^2 + bx + c = 0\), where \(a \neq 0\).
Step 2: Simplify each option.
(A) \(x^2 + 4x = 11 + x^2\)
Subtract \(x^2\) from both sides:
\[ 4x = 11 \] This is a linear equation, not quadratic.
(B) \(x^2 = 4x\)
Rearranging, \(x^2 - 4x = 0\). This is quadratic (\(a = 1, b = -4, c = 0\)).
(C) \(5x^2 = 90\)
Rearranging, \(5x^2 - 90 = 0\). This is quadratic (\(a = 5, b = 0, c = -90\)).
(D) \(2x - x^2 = x^2 + 5\)
Rearranging, \(-2x^2 + 2x - 5 = 0\). This is quadratic (\(a = -2, b = 2, c = -5\)).
Step 3: Conclusion.
Only option (A) results in a linear equation. Therefore, it is not a quadratic equation.
Final Answer: \[ \boxed{(A) \, x^2 + 4x = 11 + x^2} \]