NDA 2 2025 Maths, question 37

Topic: Algebra

Passage · Q37 to Q38

Let $f(x)=ax^{2}+bx+c$ be a quadratic polynomial such that $f(1)=f(4)=2$ . Further, $2$ is a root of $f(x)=0$ .

Q37

What is the other root of $f(x)=0$ ?

(a) $1$
(b) $2$
(c) $3$ Correct answer
(d) Cannot be determined

Solution.

Answer: (c) $3$

Equal values f(1)=f(4) place the axis at x=(1+4)/2=5/2.
The two roots are symmetric about this axis, so their sum is 5.
Since one root is 2, the other is 3.
Checking f(x)=(x−2)(x−3) satisfies the given values.