Let a, b, c be non-zero real numbers such tha | vedclass

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(C) Given the equation: $\int_0^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$.Using the property of definite integrals $\int_0^3 f(x)d

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$a + b + c = 0$

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(C) Given the equation: $\int_0^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$.Using the property of definite integrals $\int_0^3 f(x)dx = \int_0^1 f(x)dx + \int_1^3 f(x)dx$,we can rewrite the equation as:$\int_0^1 {(3ax^2 + 2bx + c)\,dx} + \int_1^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$.Subtracting $\int_1^3 {(3ax^2 + 2bx + c)\,dx}$ from both sides,we get:$\int_0^1 {(3ax^2 + 2bx + c)\,dx} = 0$.Now,evaluating the integral:$\left[ ax^3 + bx^2 + cx \right]_0^1 = 0$.Substituting the limits:$(a(1)^3 + b(1)^2 + c(1)) - (a(0)^3 + b(0)^2 + c(0)) = 0$.$a + b + c = 0$.

Let $a, b, c$ be non-zero real numbers such that $\int_0^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$,then

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