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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2005 · Mathematics · Quadratic Equation

If roots of the equation x^2-b x+c=0 be two consectutive integers,...

If roots of the equation x2−bx+c=0x^2-b x+c=0 be two consectutive integers, then b2−4cb^2-4 c equals

Options

  1. A−2-2
  2. B3
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

Let α,α+1\alpha, \alpha+1 be roots α+α+1=bα(α+1)=c∴b2−4c=(2α+1)2−4α(α+1)=1.\begin{aligned} & \alpha+\alpha+1=b \\ & \alpha(\alpha+1)=c \\ & \therefore b²-4 c=(2 \alpha+1)^2-4 \alpha(\alpha+1)=1 . \end{aligned}
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