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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2012 · Mathematics · Quadratic Equation

If the difference between the roots of a x^2+b x+c=0 is 1 , then...

If the difference between the roots of ax2+bx+c=0a x^2+b x+c=0 is 1 , then which one of the following is correct?

Options

  1. Ab2=a(a+4c)b^2=a(a+4 c)
  2. Ba2=b(b+4c)a^2=b(b+4 c)
  3. Ca2=c(a+4c)a^2=c(a+4 c)
  4. Db2=a(b+4c)b^2=a(b+4 c)

Correct answer

A. b2=a(a+4c)b^2=a(a+4 c)

Step-by-step solution

α+β=−b/aαβ=c/aα−β=1(α+β)2−(α−β)2=4αβb2a2−1=4cab2−a2a2=4cab2−a2=4acb2=a2+4ac=a(a+4c).\begin{aligned} \alpha+\beta & =-b / a \\ \alpha \beta & =c / a \\ \alpha-\beta & =1 \\ (\alpha+\beta)^2-(\alpha-\beta)^2 & =4 \alpha \beta \\ \frac{b^2}{a^2}-1 & =\frac{4 c}{a} \\ \frac{b^2-a^2}{a^2} & =\frac{4 c}{a} \\ b^2-a^2 & =4 a c \\ b^2 & =a^2+4 a c \\ & =a(a+4 c).\end{aligned}
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