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If α, β are the roots of ax2 + bx + c = 0 and −α, γ are the roots of a1x2 + b1x + c1 = 0 then β, γ are roots of Ax2 + x + C = 0, where C-1 = |
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Answer» \(\because\) α and ß are roots of ax2 + bx + c = 0 \(\therefore\) α + ß = -b/a and α ß = c/a Also, -α & \(\gamma\) are roots of a1x2 + b1x + c1 = 0 \(\therefore\) -α + \(\gamma\) = \(\frac{-b_1}{a_1}\) and -α\(\gamma\) = c1/a1 Again, ß and \(\gamma\) are roots of Ax2 + x + c = 0 \(\therefore\) ß + \(\gamma\) = -1/A ⇒ A = -(ß + \(\gamma\)) and ß\(\gamma\) = C/A \(\therefore\) C = AB\(\gamma\) = -(ß + \(\gamma\))ß\(\gamma\) (\(\because\) A = -(ß + \(\gamma\))) \(\therefore\) C-1 = \(\frac{-1}{ß\gamma(ß+\gamma)}\) |
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