What is the co-efficient?

Algebra Level 3

Let f ( x ) f(x) be a quadratic polynomial. Given, f ( 2 ) f(2) = = 10 10 and f ( − 2 ) f(-2) = = − 2 -2 .

Then, what is the coefficient of x x in f ( x ) f(x) ?


The answer is 3.

Skanda Prasad by Skanda Prasad , 20, India

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2 solutions

Skanda Prasad
Oct 25, 2016

Let f ( x ) = a x 2 + b x + c f(x)=ax^2+bx+c

Given, f ( 2 ) = 10 f(2)=10 ⟹ \implies 4 a + 2 b + c = 10 4a+2b+c=10 .... ( i ) (i)

Also, f ( − 2 ) = − 2 f(-2)=-2 ⟹ \implies 4 a − 2 b + c = − 2 4a-2b+c=-2 .... ( i i ) (ii)

Subtracting ( i i ) (ii) from ( i ) (i) , we get b = 3 b=3

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Anthony Holm
Oct 25, 2016

Because f is quadratic f(x)= ax^2+bx+c, for x=2, f=4a+2b+c=10, for x=-2, f=4a-2b+c=-2. Subtracting the two equations yields 4b=12, thus b=3.

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