Define a function f(x)=frac16 x^2-96 x+153x-3 for all real x ≠ 3 . The least positive value of f(x) is

Correct answer: (D) 24. y=frac16 x^2-96 x+153x-3 make it quadratic in x 16 x^2-x(96+y)+(153+3 y)=0 D ≥ 0 Solve y^2-576 ≥ 0 y ∈(-∞,-24] ∪[24, ∞) So, least positive is 24

Q48 / 90 · KVPY 2017 (19 Nov SB/SX) · Mathematics

Define a function $f(x)=\frac{16 x^{2}-96 x+153}{x-3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is

A
16
B
18
C
22
Correct answer
D
24

Solution

$y=\frac{16 x^{2}-96 x+153}{x-3}$ make it quadratic in $\mathrm{x}$ $\begin{array}{l} 16 x^{2}-x(96+y)+(153+3 y)=0 \\ D \geq 0 \end{array}$ Solve $y^{2}-576 \geq 0$ $\mathrm{y} \in(-\infty,-24] \cup[24, \infty)$ So, least positive is 24

Hence, the correct answer is option: 'D'.

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