Question

Which of the following equations does not have a real root?

• A. \(x^2 = 0\)
• B. \(2x - 1 = 3\)
• C. \(x^2 + 1 = 0\)
• D. \(x^3 + x^2 = 0\)

Hint:

Equations involving negative square roots have complex roots, not real.

Answer 1

The Correct Option is C

Problem:
Determine which equation lacks a real root.

Solution:
A quadratic equation \(ax^2 + bx + c = 0\) has real roots if the discriminant \(D = b^2 - 4ac \geq 0\).

Consider the equation \(x^2 + 1 = 0\). Here, \(a = 1\), \(b = 0\), and \(c = 1\).
Calculate the discriminant:
\[D = 0^2 - 4 \times 1 \times 1 = -4\]

Since \(D = -4 < 0\), this equation has no real roots.

Answer:
\[\boxed{x^2 + 1 = 0}\]