Discussion

Explanation:

α and β are the roots of the equation 2x² + 3x + 1 = 0

∴ Sum of the roots = α + β = -3/2   …(1)
& product of the roots = αβ = ½   …(2)

Now, a quadratic equation whose roots are α² and β² is
x² – (α² + β²)x + α² × β² = 0

Now, α² + β² = (α + β)² - 2αβ = 9/4 – 1 = 5/4

∴ The required quadratic equation is: 
x² – (α² + β²)x + (αβ)² = 0

⇒ x² – 5x/4 + 1/4 = 0

⇒ 4x² – 5x + 1 = 0

Hence, option (a).

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