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Sagot :
Answer:
[tex]2(x^3-5x^2+7x-3)=2x^3-10x^2+14x-6[/tex]Explanation:
Here, we want to get the polynomial function
We expect 3 roots
This means there should be 3 x-intercepts
One of the intercepts has an even multiplicity, that means it occurred twice 9since our maximum occurrence is 3)
The general form of the degree 3 polynomial is:
[tex]f(x)=ax^3+bx^2\text{ + cx + d}[/tex]where d is the y-intercept. This is the value of f(x) when x is zero
Let us take a look at the x-intercepts:
We have them as:
(x-1)(x-1)(x-3)
Opening up these brackets, we have:
[tex]\begin{gathered} (x-1)(x-1)(x-3)\text{ = } \\ (x-3)(x^2-2x\text{ + 1)} \\ =x^3-2x^2+x-3x^2\text{ + 6x - 3} \\ =x^3-5x^2+7x-3 \end{gathered}[/tex]Recall, the y-intercept is -6
We have to multiply the whole expression by 2 as follows:
[tex]2(x^3-5x^2+7x-3)[/tex]
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