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Question

The function $$x^2 + px + q$$ with $$p$$ and $$q$$ greater than the zero has its minimum value when:


A
x=p
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B
x=p2
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C
x=2p
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D
x=p24q
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Solution

The correct option is C $$x = \dfrac{-p}{2}$$
$$Let\quad f(x)={ x }^{ 2 }+px+q\\ p,q>0$$
$${ ax }^{ 2 }+bx+c$$ has its minimum value at $$x=-\cfrac { b }{ 2a }$$
Here, a=1, b=p, c=q.
$$\therefore f(x)$$ has its minimum value at $$x=-\cfrac { p }{ 2(1) } = -\cfrac{p}{2}$$  

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