Question

The equation whose roots are the squares of the roots of the equation \( 2x^2 + 3x + 1 = 0 \) is:

• A. \( 4x^2 + 5x + 1 = 0 \)
• B. \( 4x^2 - x + 1 = 0 \)
• C. \( 4x^2 - 5x - 1 = 0 \)
• D. \( 4x^2 - 5x + 1 = 0 \)
• E. \( 4x^2 + 5x - 1 = 0 \)

Hint:

To find the equation with squared roots, just solve $ax^2 + c = -bx$, then square both sides: $a^2x^4 + 2acx^2 + c^2 = b^2x^2$. Finally, replace $x^2$ with $y$.

Answer 1

The Correct Option is D