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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2025 · Mathematics · Quadratic Equation

For the following two (02) items: Let f(x) = ax^2 + bx + c be a...

For the following two (02) items:
Let f(x)=ax2+bx+cf(x) = ax^2 + bx + c be a quadratic polynomial such that f(1)=f(4)=2f(1) = f(4) = 2. Further, 2 is a root of f(x)=0f(x) = 0.

What is (a+b+c)(a + b + c) equal to?

Options

  1. A00
  2. B11
  3. C22
  4. DCannot be determined

Correct answer

C. 22

Step-by-step solution

Given f(x)=ax2+bx+cf(x) = ax^2 + bx + c

Substituting x=1x = 1 in the given polynomial:

f(1)=a(1)2+b(1)+c=a+b+cf(1) = a(1)^2 + b(1) + c = a + b + c

It is given in the problem that f(1)=2f(1) = 2.

Therefore, a+b+c=2a + b + c = 2.

Answer: 22
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