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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2019 · Mathematics · Quadratic Equation

Paragraph: Let f(x)=x^2+2 x-5 and g(x)=5 x+30 Question: What are...

Paragraph: Let f(x)=x2+2x−5f(x)=x^2+2 x-5 and g(x)=5x+30g(x)=5 x+30
Question: What are the roots of the equation g[f(x)]=0g[f(x)]=0 ?

Options

  1. A1,−11,-1
  2. B−1,−1-1,-1
  3. C1,1
  4. D0,1

Correct answer

B. −1,−1-1,-1

Step-by-step solution

f(x)=x2+2x−5g(x)=5x+30g[f(x)]=0⇒5f(x)+30=0⇒f(x)+6=0⇒x2+2x−5+6=0⇒x2+2x+1=0⇒x=−1,−1\begin{aligned} & f(x)=x^2+2 x-5 \\ & g(x)=5 x+30 \\ & g[f(x)]=0 \\ & \Rightarrow 5 f(x)+30=0 \\ & \Rightarrow f(x)+6=0 \\ & \Rightarrow x^2+2 x-5+6=0 \\ & \Rightarrow x^2+2 x+1=0 \\ & \Rightarrow x=-1,-1\end{aligned}
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