The roots of the equation x 2 +px+q=0 are 1 and 2, the roots of the equation qx 2 -px+1=0 must be

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CollectorBabu · Accepted Answer

Given equation: x2 + px + q = 0 Say roots are α and β . We know that, Sum of the roots = –p = 1 + 2 ⇒ p = –3. Product of the roots = q = 1 × 2 ⇒ q = 2. From another equation qx2 – px + 1 = 0. Sum of the roots = α + β = p/q = -3/2…………..(1) And Products of roots, α . β = 1/q = ½ Now, ( α – β ) 2 = ( α + β ) 2 - 4 α . Β Putting values of α + β and α . Β , we got, ( α – β ) 2 = (-3/2) 2 – 4*(1/2) ( α – β ) 2 = ¼ α – β = ½…………………….(2) From 1 and 2, α + β = -3/2 and α – β = ½ Solving this we got, α   = -1/2 β = -1 Hence option C is correct answer.

The roots of the equation x 2 +px+q=0 are 1 and 2, the roots of the equation qx 2 -px+1=0 must be

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