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Given that f(x)=4x3-12x2+10 and g(x)=x3 – 2x2 + 5x

The value of f(x)- g(x)= ax'+bx?+ cx+d. What are the values of the coefficients a,b,c,d?

1 Answer

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Answer:

The values of a,b,c and d are as follows:

a = 3, b = -12, c = -5, d = 10

Explanation:

Given functions are:


f(x) = 4x^3-12x^2+10\\g(x) = x^3-2x^2+5x

We have to find the value of f(x) - g(x). This means we have to subtract function g(x) from function f(x)

So,


f(x) - g(x) = (4x^3-12x^2+10)-(x^3-2x^2+5x)\\= 4x^3-12x^2+10-x^3+2x^2-5x

Combining alike terms


= 4x^3-x^3-12x^2+2x^2-5x+10\\= 3x^3-10x^2-5x+10

Now it was given that:

f(x)- g(x)= ax^3+bx^2+ cx+d

By comparing both we get

a = 3, b = -12, c = -5, d = 10

Hence,

The values of a,b,c and d are as follows:

a = 3, b = -12, c = -5, d = 10

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