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g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" a...

`g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4.`
Number of real roots of the equation g(x) = 0 is

A

2

B

0

C

1

D

3

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To solve the problem, we start with the functional equation given: \[ g(x+y) = g(x) + g(y) + 3xy(x+y) \] for all \( x, y \in \mathbb{R} \), and we know that \( g'(0) = -4 \). ### Step 1: Differentiate the functional equation ...
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