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

Correct Answer: 4.5

Explanation:

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


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