Question

f est une fonction polynome du second degres dont les racines sont -4 et 5. De plus, on sait que f(3)=8. determiner la forme developpée de f(x)

Answer 1

Explanation:

To determine the expanded form of the polynomial function f(x), we can use the fact that it is a quadratic function with roots at -4 and 5. The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

We know that the roots of the function are -4 and 5. This means that (x - (-4)) and (x - 5) are factors of the function. Simplifying, we get (x + 4) and (x - 5) as the factors.

To find the expanded form, we can multiply these factors together:

f(x) = (x + 4)(x - 5)

Expanding this expression using the distributive property:

f(x) = x(x - 5) + 4(x - 5)

Multiplying each term:

f(x) = x^2 - 5x + 4x - 20

Combining like terms:

f(x) = x^2 - x - 20

Therefore, the expanded form of the polynomial function f(x) is f(x) = x^2 - x - 20.