The coefficients for the polynomial with degree 3, roots: x = 2, x =
-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.
It is given that the polynomial is of degree 3 and its roots are,
x = 2
x = -1
x = 3
Thus, the factors of the polynomial would be,
(x - 2), (x + 1), and (x - 3)
The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,
(x - 2)(x + 1)(x - 3)
= (x² -2x + x -2)(x - 3)
= (x² -x -2)(x - 3)
= x³ - 3x² - x² + 3x - 2x + 6
= x³ - 4x² + x + 6
= x³ + (-4)x² + x + 6
Hence, the required coefficients of the polynomial are, (-4) and 6.
Learn more about a polynomial here:
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