The least value of the quadratic polynomial, f x = 2 p 2 + 1 x 2 + 2 4 p 2 - 1 x + 4 2 p 2 + 1 for real values of p and x is

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Question: Answered & Verified by Expert

The least value of the quadratic polynomial,

f (x) = (2 p^{2} + 1) x^{2} + 2 (4 p^{2} - 1) x + 4 (2 p^{2} + 1)

for real values of

p

and

x

is

MathematicsCircleJEE Main

Solution:

1757 Upvotes Verified Answer

The correct answer is: 3

y = 2 p^{2} (x^{2} + 4x + 4) + x^{2} - 2 x + 1 + 3

y = 2 p^{2} {(x + 2)}^{2} + {(x - 1)}^{2} + 3

p = 0, x = 1

y_{min} = 3

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