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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2011 · Mathematics · Quadratic Equation

If sum of squares of the roots of the equation x^2+k x-b=0 is 2 b ,...

If sum of squares of the roots of the equation x2+kx−b=0x^2+k x-b=0 is 2b2 b, what is kk equal to?

Options

  1. A1
  2. Bbb
  3. C−b-b
  4. D0

Correct answer

D. 0

Step-by-step solution

Let α,β\alpha, \beta be two roots then α2+β2=2b (given)  Now α+β=−k1=−k=−b1=−b⇒α2+β2=(α+β)2−2αβ⇒2b=k2−2(−b)⇒2b=k2+2b⇒k2=0⇒k=0.\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}
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