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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2011 · Mathematics · Quadratic Equation

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

If the roots of the equation 3x2−5x+q=03 x^2-5 x+q=0 are equal, then what is the value of qq ?

Options

  1. A22
  2. B5/125 / 12
  3. C12/2512 / 25
  4. D25/1225 / 12

Correct answer

D. 25/1225 / 12

Step-by-step solution

∵\because Roots are equal ∴D=03x2−5x+q=0∴x\therefore \mathrm{D}=03 x^2-5 x+q=0 \quad \therefore x roots are −b2a=56Product\frac{-b}{2 a}=\frac{5}{6}Product of roots =ca=q3\frac{c}{a}=\frac{q}{3}56×56=q32536=q3⇒q=2512.\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}$
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