Answer:
x = -1 (multiplicity 2)
Explanation:
Given the cubic f(x) = x³ -x² -5x -3 has x=3 as a root, you want the other roots.
Quadratic factor
You can find the quadratic factor of the polynomial using synthetic division. That tells you ...
f(x) = (x -3)(x² +2x +1)
You recognize the quadratic factor as the perfect square trinomial ...
x² +2x +1 = (x +1)²
Roots
The remaining roots will be the values of x that make these factors zero:
x +1 = 0 ⇒ x = -1 . . . . . and the other is the same: multiplicity 2
The remaining roots are x=-1 and x=-1.
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Additional comment
We find a graphing calculator to be a quick and easy way to find the real roots of higher-degree polynomials. They are shown in the second attachment.