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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2024 · Mathematics · Quadratic Equation

What is the number of real roots of the equation...

What is the number of real roots of the equation (x−1)2+(x−3)2+(x−5)2=0?(x-1)^2+(x-3)^2+(x-5)^2=0 ?

Options

  1. ANone
  2. BOnly one
  3. COnly two
  4. DThree

Correct answer

A. None

Step-by-step solution

Given that, (x−1)2+(x−3)2+(x−5)2=0(x-1)^2+(x-3)^2+(x-5)^2=0⇒x2−2x+1+x2−6x+9+x2−10x+25=0⇒3x2−18x+35=0\begin{aligned} & \Rightarrow x^2-2 x+1+x^2-6 x+9+x^2-10 x+25=0 \\ & \Rightarrow 3 x^2-18 x+35=0 \end{aligned}$DiscriminantDiscriminant\mathrm{D}=(-18)^2-4 \times 3 \times 35=-96 < 0\because$ Discriminant is negative. So, the given equation does not have any real roots.
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