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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2013 · Mathematics · Quadratic Equation

What is the difference in the roots of the equation x^2-10 x+9=0 ?

What is the difference in the roots of the equation x2−10x+9=0?x^2-10 x+9=0 ?

Options

  1. A2
  2. B3
  3. C5
  4. D8

Correct answer

D. 8

Step-by-step solution

Sum of roots α+β=10\alpha+\beta=10 Product of roots α⋅β=9\alpha \cdot \beta=9α−β=(α+β)2−4α⋅β=(10)2−4×9=100−36=64α−β=8\begin{aligned} \alpha-\beta & =\sqrt{(\alpha+\beta)^2-4 \alpha \cdot \beta} \\ & =\sqrt{(10)^2-4 \times 9} \\ & =\sqrt{100-36}=\sqrt{64} \\ \alpha-\beta & =8 \end{aligned}$DifferenceofrootsDifference of roots=8$.
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