Let be the roots of the equation ,

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let α,β\alpha, \beta be the roots of the equation px2+qx+r=0px^2 + qx + r = 0, p≠0p \neq 0. If p,q,rp, q, r are in AP and 1α+1β=4\frac{1}{\alpha} + \frac{1}{\beta} = 4, the value of ∣α−β∣|\alpha - \beta| is (1) 349\frac{\sqrt{34}}{9} (2) 2139\frac{2\sqrt{13}}{9} (3) 619\frac{\sqrt{61}}{9} (4) 2179\frac{2\sqrt{17}}{9}

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