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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2021 · Mathematics · Quadratic Equation

Consider all the real roots of the equation x^4-10 x^2+9=0 . What...

Consider all the real roots of the equation x4−10x2+9=0x^4-10 x^2+9=0. What is the sum of the absolute values of the roots?

Options

  1. A4
  2. B6
  3. C8
  4. D10

Correct answer

C. 8

Step-by-step solution

x4−10x2+9=0⇒x4−9x2−x2+9=0⇒x2(x2−9)−1(x2−9)=0⇒(x2−9)(x2−1)=0⇒x2−9=0 or  x2−1=0⇒x=±3 or x=±1\begin{aligned} & x^4-10 x^2+9=0 \\ & \Rightarrow x^4-9 x^2-x^2+9=0 \\ & \Rightarrow x^2\left(x^2-9\right)-1\left(x^2-9\right)=0 \\ & \Rightarrow\left(x^2-9\right)\left(x^2-1\right)=0 \\ & \Rightarrow x^2-9=0 \text{\text{ or } } x^2-1=0 \\ & \Rightarrow x= \pm 3 \text{ or } x= \pm 1 \end{aligned} Sum of the absolute values of the roots =3+(−3)+1+(−1)=8=3+(-3)+1+(-1)=8
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