Quadratic Equations · NDA previous year questions

2014 3 questions

1. Q82014 · 28 Sept 2014

   Every quadratic equation $a{x}^2+bx+c=0$ where $a,b,c\in \mathbf{R},a\ne 0$ has

   1. A.exactly one real root.
   2. B.at least one real root.
   3. C.at least two real roots.
   4. D.at most two real roots.
   Show answer

   Answer: D

2. Q92014 · 28 Sept 2014

   If $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$ and $\alpha +h,\beta +h$ are the roots of $p{x}^2+qx+r=0$, then what is h equal to ?

   1. A.$\frac{1}{2}\left(\frac{b}{a}-\frac{q}{p}\right)$
   2. B.$\frac{1}{2}\left(-\frac{b}{a}+\frac{q}{p}\right)$
   3. C.$\frac{1}{2}\left(\frac{b}{p}+\frac{q}{a}\right)$
   4. D.$\frac{1}{2}\left(-\frac{b}{p}+\frac{q}{a}\right)$
   Show answer

   Answer: A

3. Q132014 · 20 Apr 2014

   If $\alpha$ and $\beta$ are the roots of the equation $a{x}^2+bx+c=0$, where $a\ne 0$, then $(a\alpha +b)(a\beta +b)$ is equal to:

   1. A.$ab$
   2. B.$bc$
   3. C.$ca$
   4. D.$abc$
   Show answer

   Answer: C