Question

If α and β are the zeroes of the quadratic 
polynomial p(x)=3x2+2x-6, then find the 
value of  α - β.
Select one:
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Answer 1

sum of zeroes = α + β = -b/a = -2/3

product = αβ = c /a = -6 / 3 = -1/2  

  ⇒ (α + β )² = α² +β² + 2αβ

 ⇒ (-2/3)² = α² +β² + 2 x -1/2

 ⇒ α² + β² = 4/9 + 1 = 13 / 9

 ∴ ( α - β )² = α² +β² - 2αβ

  ⇒ ( α - β) = √13/9 -2 x -1/2

  ⇒ α - β = √ 13/9 + 1

  ⇒ α - β = √ 22/9

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