If the roots of x2 - ax + b = 0 differ by unity, then we get ____.

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From the equation, we get, Let the 2 roots be α and (α + 1) α + β = a ⇒ α + (α + 1) = a ⇒ α = (a-1)/2 Similarly, α β = b ⇒ α(α+1)=b ⇒ [(a-1)/2] [(a-1)/2]+1 = b ⇒ (a – 1)(a+1) = 4b ⇒ a2 -1=4b

If α and β are the roots of the equation 3 x2 + 2x + 7 = 0, then 1/α+1/β=____.

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Let α and β be the roots of the equation. Then, α + β = -b/a = -2/3 and αβ = c/a = 7/3 1/α + 1/β=(α + β) /αβ = -2/3 × 3/7 = -2/7

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CBSE Class 11th Math 5 - Complex Numbers and Quadratic Equations MCQs
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