The difference in the roots of the equation 2x2

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The difference in the roots of the equation 2x² - 11x + 5 = 0 is

1. 4.5
2. 4
3. 3.5
4. 3

Correct Option: A

Let α and β be the roots of the quadratic equation 2x² - 11x + 5 = 0
∴ α + β = -(-11)/2 = 11/2 ...(i)
and αβ = 5/2
Now, (α - β)² = (α + β)² - 4αβ
= (11/2)² - 4(5/2) = 121/4 - 20/2
= 121 - 40/4 = 81/4 = (9/2)²
∴ Difference of roots = (α - β) = 9/2 = 4.5