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

KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 5 of 120

Marks: +1, -0

Define a function

\f (x) = {16x ^2- 96x +153}/{x-3}

forall real x ≠ 3. The least positive value of f(x) is

Solution:

y= {16x ^2- 96x +153}/{x-3}

make it quadratic in x

16 x^2-x (96 + y) + (153 + 3y) = 0

D ≥ 0
Solve

y^2-576 ≥ 0

y ∈ (– ∞, –24] ∪ [24, ∞)

So, least positive is 24

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