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Question

If the roots of x2-bx+c=0 are two consecutive integers, then b2 − 4 c is
(a) 0
(b) 1
(c) 2
(d) none of these.


Solution

(b) 1

Given equation: x2 - bx + c = 0
Let α and α+1 be the two consecutive roots of the equation.

Sum of the roots = α + α + 1 = 2α + 1  
Product of the roots = α (α + 1)=α2 + α


 So, sum of the roots= 2α+1=-Coeffecient of xCoeffecient of x2=b1=bProduct of the roots= α2+α=Constant termCoeffecient of x2=c1=cNow, b2-4c=2α+12-4α2+α=4α2+4α+1-4α2-4α=1    

Mathematics
RD Sharma XI (2015)
Standard XI

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