SOLUTION: Find a third degree polynomial that has x=1 as its only real zero and this zero has a: multiplicity one (1) b: multiplicity three (3)

Question 734187: Find a third degree polynomial that has x=1 as its only real zero and this zero has a: multiplicity one (1) b: multiplicity three (3)
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
All third degree polynomials have three roots. If x=1 is a root, the polynomial can be factored so that (x-1) is a factor.

If it is the only real root, and it's multiplicity one, that means that the other two roots are imaginary, and are also conjugates. The simplest pair of imaginary conjugate roots are i and -i. The quadratic equation with roots i and -i is (x+i)(x-i) = 0, or x^2+1 = 0.

The third degree polynomial with 1, i and -i as roots is (x-1)(x^2+1) = 0, or x^3-x^2+x-1 = 0. There are other solutions, depending on what imaginary roots you use.

If 1 has multiplicity three, that means that it is a triple root. The one and only one cubic equation with a root of 1 that has multiplicity three is (x-1)(x-1)(x-1) = 0, or x^3-3x^2+3x-1.
RELATED QUESTIONS
Find a third degree polynomial that has x=1 as its only real zero and this zero has: A.... (answered by josgarithmetic)

find a third degree polynomial that has x=1 as its only real zero and this zero has:... (answered by josgarithmetic)

Find a polynomial that has the following characteristics. Show your work. -Its... (answered by MathLover1)

Find a polynomial of lowest possible degree that has 2 as a zero of multiplicity 3, and... (answered by MathLover1)

Find a polynomial function with leading coefficient 1 that has the given zeros,... (answered by Alan3354)

Find a polynomial function with leading coefficient 1 that has the given zeros,... (answered by greenestamps)

Find the equation of a third degree polynomial that has a zero at -1 and a multiplicity... (answered by Fombitz)

Find a polynomial function f(x) of least degree having only real coefficients and... (answered by ikleyn)

find a three degree polynomial with x=1 as its only real zero and its zero has: a.... (answered by josgarithmetic)