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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2019 · Mathematics · Quadratic Equation

Which one of the following is the second degree polynomial function...

Which one of the following is the second degree polynomial function f(x)f(x) where f(0)=5,f(−1)=10f(0)=5, f(-1)=10 and f(1)=6f(1)=6 ?

Options

  1. A5x2−2x+55 x^2-2 x+5
  2. B3x2−2x−53 x^2-2 x-5
  3. C3x2−2x+53 x^2-2 x+5
  4. D3x2−10x+53 x^2-10 x+5

Correct answer

B. 3x2−2x−53 x^2-2 x-5

Step-by-step solution

f(x)=ax2+bx+cf(0)=5⇒c=5⋯(i)f(−1)=10⇒a−b=5⋯(ii)f(1)=6⇒a+b=6⋯(iii)\begin{aligned} & f(x)=a x^2+b x+c \\ & f(0)=5 \Rightarrow c=5 \cdots(i)\\ & f(-1)=10 \Rightarrow a-b=5 \cdots(ii)\\ & f(1)=6 \Rightarrow a+b=6 \cdots(iii) \end{aligned} from (ii) \& (iii) we get, a=3b=−2∴a=3b=-2\therefore quadratic equation is 3x2−2x+5=03 x^2-2 x+5=0
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