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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2011 · Mathematics · Quadratic Equation

If one of the roots of the equation a(b-c) x^2+b(c-a) x+c(a-b)=0 is...

If one of the roots of the equation a(b−c)x2+b(c−a)x+c(a−b)=0a(b-c) x^2+b(c-a) x+c(a-b)=0 is 1 , what is the second root?

Options

  1. A−b(c−a)a(b−c)-\frac{b(c-a)}{a(b-c)}
  2. Bb(c−a)a(b−c)\frac{b(c-a)}{a(b-c)}
  3. Cc(a−b)a(b−c)\frac{c(a-b)}{a(b-c)}
  4. D−c(a−b)a(b−c)-\frac{c(a-b)}{a(b-c)}

Correct answer

C. c(a−b)a(b−c)\frac{c(a-b)}{a(b-c)}

Step-by-step solution

Let other root is β\beta of the equation a(b−c)x2+b(c−a)x+c(a−b)=0a(b-c) x^2+b(c-a) x+c(a-b)=0 product of roots =ca1×β=c(a−b)a(b−c)∴=\frac{c}{a}1 \times \beta=\frac{c(a-b)}{a(b-c)}\therefore \quad other root (β)=c(a−b)a(b−c)(\beta)=\frac{c(a-b)}{a(b-c)}.
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