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If x is real then the minimum value of \( \Large \left(x^{2}-x-1\right) \) is

A) \( \Large \frac{3}{4} \)
B) 0
C) 1
D) \( \Large -\frac{5}{4} \)

Correct Answer:




D) \( \Large -\frac{5}{4} \)

Description for Correct answer:
\( \Large x^{2}-x-1 \)

=> If \( \Large ax^{2}+bx+c=0 \)

Then minimum value of equation is \( \Large \left(\frac{4ac-b^{2}}{4a}\right) \)

Because, in the given equation,

a = 1, b = -1, = -1

Therefore minimum value

=> \( \Large \frac{ \left(4 \times 1 \times \left(-1\right) \right) \left(-1\right)^{2} }{4 \times 1} \)

= \( \Large \frac{-4-1}{4} = -\frac{5}{4} \)

Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics

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