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Question
lf roots of the equation x2− bx +c=0 be two consectutive integers, then b2−4c equals
lf roots of the equation x2− bx +c=0 be two consectutive integers, then b2−4c equals
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Solution
The correct option is D 1
Let α, α+1 be roots of x2−bx+c=0, thensum of roots α+α+1=b
and product of roots α(α+1)=c
.∴b2−4c=(2α+1)2−4α(α+1)=1.
Let α, α+1 be roots of x2−bx+c=0, then
sum of roots α+α+1=b
and product of roots α(α+1)=c
.∴b2−4c=(2α+1)2−4α(α+1)=1.
and product of roots α(α+1)=c
.∴b2−4c=(2α+1)2−4α(α+1)=1.
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