Q253 / 270 · NDA 2011 (Phase 2) · Mathematics

If the roots of the equation $3 x^2-5 x+q=0$ are equal, then what is the value of $q$ ?

  • A
    $2$
  • B
    $5 / 12$
  • C
    $12 / 25$
  • Correct answer
    D
    $25 / 12$

Solution

$\because$ Roots are equal $\therefore \mathrm{D}=0$ $3 x^2-5 x+q=0 \quad \therefore x$ roots are $\frac{-b}{2 a}=\frac{5}{6}$ Product of roots $=\frac{c}{a}=\frac{q}{3}$ $\begin{aligned} \frac{5}{6} \times \frac{5}{6} & =\frac{q}{3} \\ \frac{25}{36} & =\frac{q}{3} \quad \Rightarrow q=\frac{25}{12} .\end{aligned}$

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

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