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Calculus Level 2

If f ( x ) = a x 2 + b x + c f(x) = ax^2 + bx + c has 2 distinct real roots p p and q q , then find the value of f ′ ′ ( p + q ) f''(p+q) in terms of a , b a,b and/or c c .

a + b + c a+b+c 1 1 c c − b a \frac{-b}{a} − a b \frac{-a}{b} b b 2 a 2a c a \frac{c}{a}

Mohamad Zare by Mohamad Zare , 23, Iran

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1 solution

Mohamad Zare
Mar 24, 2016

f ′ ( x ) = 2 a x f'(x)=2ax and f ′ ′ ( x ) = 2 a f''(x)=2a so f ′ ′ ( p + q ) = 2 a f''(p+q)=2a

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