A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is: [tex]3x^2-15x+12[/tex]
An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
For this case we have that the following function complies with the given conditions:
[tex]f(x)=3x^2-15x+12[/tex]
To prove it, let's find the roots of the polynomial:
[tex]3x^2-15x+12=0[/tex]
By doing common factor 3 we have:
[tex]3(x^2-5x+4)=0[/tex]
Factoring the second degree polynomial we have:
[tex]3(x-1)(x-4)=0[/tex]
Then, the solutions are:
Solution 1:
[tex]x-1=0 \ or \ x=1[/tex]
Solution 2:
[tex]x-4=0\ \ or \ x=4[/tex]
Hence A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:[tex]3x^2-15x+12[/tex]
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