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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2015 · Mathematics · Quadratic Equation

In solving a problem that reduces to a quadratic equation, one...

In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds -9 and -1 for roots. The correct equation is

Options

  1. Ax2−10x+9=0x^2-10 x+9=0
  2. Bx2−10x+9=0x^2-10 x+9=0
  3. Cx2−10x+16=0x^2-10 x+16=0
  4. Dx2−8x−9=0x^2-8 x-9=0

Correct answer

A. x2−10x+9=0x^2-10 x+9=0

Step-by-step solution

Let correct equation is ax2+bx+c=0a x^2+b x+c=0 According to first student, equation is: ax2+bx+c1=0a x^2+b x+c_1=0 and roots are 8 and 2 8+2=−ba⇒ba=−108+2=\frac{-b}{a} \Rightarrow \frac{b}{a}=-10 Quadratic equation according to second student ax2+b1x+c=0\mathrm{ax}^2+\mathrm{b}_1 \mathrm{x}+\mathrm{c}=0 and roots are -9 and -1 (−9)×(−1)=ca⇒ca=9(-9) \times(-1)=\frac{c}{a} \Rightarrow \frac{c}{a}=9 Putting value in original equation x2+bax+ca=0x2−10x+9=0\begin{aligned} & x^2+\frac{b}{a} x+\frac{c}{a}=0 \\ & x^2-10 x+9=0 \end{aligned}
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