Q178 / 270 · NDA 2013 (Phase 2) · Mathematics

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

  • A
    2
  • B
    3
  • C
    5
  • Correct answer
    D
    8

Solution

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

Hence, the correct answer is option: 'D'.

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