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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2012 · Mathematics · Quadratic Equation

For the next Two (2) questions that follow: The equation formed by...

For the next Two (2) questions that follow: The equation formed by multiplying each root of ax2+bx+c=0a x^2+b x+c=0 by 2 is x2+36x+24=0x^2+36 x+24=0. The equation formed by multiplying each root of ax2+bx+c=0a x^2+b x+c=0 by 2 is x2+36x+24=0x^2+36 x+24=0. What is b:cb: c equal to?

Options

  1. A3:13: 1
  2. B1:21: 2
  3. C1:31: 3
  4. D3:23: 2

Correct answer

A. 3:13: 1

Step-by-step solution

Let α,β\alpha, \beta be roots of equation ax2+bx+c=0∴α+β=−b/aαβ=c/a\begin{aligned} a x^2+b x+c & =0 \\ \therefore \quad \alpha+\beta & =-b / a \\ \alpha \beta & =c / a \end{aligned} So, 2α2 \alpha and 2β2 \beta we roots of equation x2+36x+24=02α+2β=−36α+β=−18⇒−ba=−18⇒b=18a⇒(2α)+(2β)=24αβ=6ca=6⇒c=6a∴b:c=3:1.\begin{aligned} x^2+36 x+24 & =0 \\ 2 \alpha+2 \beta & =-36 \\ \alpha+\beta & =-18 \\ \Rightarrow \quad \frac{-b}{a} & =-18 \Rightarrow b=18 a \\ \Rightarrow \quad(2 \alpha)+(2 \beta) & =24 \\ \alpha \beta & =6 \\ \frac{c}{a} & =6 \Rightarrow c=6 a \\ \therefore b: c=3: & 1 . \end{aligned}
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