Q208 / 270 · NDA 2011 (Phase 1) · Mathematics

If sum of squares of the roots of the equation $x^2+k x$ $-b=0$ is $2 b$, what is $k$ equal to?

  • A
    1
  • B
    $b$
  • C
    $-b$
  • Correct answer
    D
    0

Solution

Let $\alpha, \beta$ be two roots then $\begin{array}{rlrl} & & \alpha^2+\beta_2 & =2 b \text { (given) } \\ \text { Now } & & \alpha+\beta & =-\frac{k}{1}=-k \\ & & & =\frac{-b}{1}=-b \\ \Rightarrow & & \alpha^2+\beta^2 & =(\alpha+\beta)^2-2 \alpha \beta \\ \Rightarrow & & 2 b & =k^2-2(-b) \\ \Rightarrow & & 2 b & =k^2+2 b \\ \Rightarrow & k^2 & =0 \Rightarrow k=0 . \end{array}$

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

Relevant Questions