Step-by-Step Solution
Key Concept: Expand as $x^4 + 2x^2 + 1 - x^2 = x^4 + x^2 + 1 = 0$. Since $x^4 \geq 0$ and $x^2 \geq 0$, $x^4 + x^2 + 1 \geq 1 > 0$ for all real $x$.
Stepwise Solution:
Expand: $x^4 + 2x^2 + 1 - x^2 = 0 \Rightarrow x^4 + x^2 + 1 = 0$. [0.5 Mark]
For any real number $x$, $x^2 \geq 0$ and $x^4 \geq 0$, so $x^4 + x^2 + 1 \geq 1 > 0$. It can never equal $0$ for real $x$. Hence, no real roots. [0.5 Mark]
Marking Scheme:
• Expanding to $x^4 + x^2 + 1 = 0$: 0.5 Mark
• Arguing $x^4 + x^2 + 1 > 0$ for all real $x$: 0.5 Mark
Correct Answer: No real roots