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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2012 · Mathematics · Quadratic Equation

What is the sum of the squares of the roots of the equation x^2+2...

What is the sum of the squares of the roots of the equation x2+2x−143=0x^2+2 x-143=0 ?

Options

  1. A170
  2. B180
  3. C190
  4. D290

Correct answer

D. 290

Step-by-step solution

If roots α,β\alpha, \beta then α+β=−2αβ=−143α2+β2=(α+β)2−2αβ=(−2)2−2(−143)=4+286=290.\begin{aligned} \alpha+\beta & =-2 \\ \alpha \beta & =-143 \\ \alpha^2+\beta^2 & =(\alpha+\beta)^2-2 \alpha \beta \\ & =(-2)^2-2(-143) \\ & =4+286=290. \end{aligned}
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