1.

If α and β are the roots of the equation 3x2 – 11x + 6, then find the value of (α – β)2.1. 49/92. 36/73. 64/74. 81/7

Answer» Correct Answer - Option 1 : 49/9

Given:

α and β are the roots of the equation 3x2 – 11x + 6

Formula Used:

If ax2 + bx + c = 0, then

Sum of the roots = -(b/a)

Product of the roots = (c/a)

(a – b)2 = (a + b)2 – 4 × a × b

Calculation:

For equation, 3x2 – 11x + 6

a = 3, b = -11, and c = 6

The sum of the roots = -(b/a)

⇒ α + β = -(-11/3)

⇒ α + β = 11/3

The product of the roots = (c/a)

⇒ α × β = 6/3

⇒ α × β = 2

Now, (α - β)2 = (α + β)2 – 4 × α × β

⇒ (11/3)2 – 4 × 2

⇒ (121/9) – 8

⇒ (121 – 72)/9

⇒ 49/9

∴ The value of (α - β)2 is 49/9.


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