A degree 4 polynomial P(x) with integer coefficients has zeros and 4, with 4 being a zero of multiplicity 2. Moreover, the coefficient of x4 is 1. Find the polynomial. Note: The polynomial must be expanded so that no imaginary number i appears in the polynomial. Note:
Solution
1.COEFFICIENTS ARE REAL ..SO IF 3I IS A ROOT ..THEN -3I IS ANOTHER ROOT ....SO PLYNOMIAL = P = [X-3I][X+3I][F(X)]=[X^2+9][F(X)]......F[X] HAS ZERO OF MULTIPLICITY 2 ..SO ...
P=[X^2+9][X-4]^2 =[X^2+9][X^2-8X+16]=X^4-8X^3+25X^2-72X+144 ....ANSWER
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A degree 4 polynomial with integer coefficients has zeros and 4- wit.docx
1. A degree 4 polynomial with integer coefficients has zeros and 4, with 4 being a zero
of multiplicity 2. Moreover, the coefficient of is 1. Find the polynomial. Note: The
polynomial must be expanded so that no imaginary number appears in the polynomial.
Note: and .
A degree 4 polynomial P(x) with integer coefficients has zeros and 4, with 4 being a zero of
multiplicity 2. Moreover, the coefficient of x4 is 1. Find the polynomial. Note: The
polynomial must be expanded so that no imaginary number i appears in the polynomial.
Note:
Solution
1.COEFFICIENTS ARE REAL ..SO IF 3I IS A ROOT ..THEN -3I IS ANOTHER ROOT ....SO
PLYNOMIAL = P = [X-3I][X+3I][F(X)]=[X^2+9][F(X)]......F[X] HAS ZERO OF
MULTIPLICITY 2 ..SO ...
P=[X^2+9][X-4]^2 =[X^2+9][X^2-8X+16]=X^4-8X^3+25X^2-72X+144 ....ANSWER
![A degree 4 polynomial with integer coefficients has zeros and 4, with 4 being a zero
of multiplicity 2. Moreover, the coefficient of is 1. Find the polynomial. Note: The
polynomial must be expanded so that no imaginary number appears in the polynomial.
Note: and .
A degree 4 polynomial P(x) with integer coefficients has zeros and 4, with 4 being a zero of
multiplicity 2. Moreover, the coefficient of x4 is 1. Find the polynomial. Note: The
polynomial must be expanded so that no imaginary number i appears in the polynomial.
Note:
Solution
1.COEFFICIENTS ARE REAL ..SO IF 3I IS A ROOT ..THEN -3I IS ANOTHER ROOT ....SO
PLYNOMIAL = P = [X-3I][X+3I][F(X)]=[X^2+9][F(X)]......F[X] HAS ZERO OF
MULTIPLICITY 2 ..SO ...
P=[X^2+9][X-4]^2 =[X^2+9][X^2-8X+16]=X^4-8X^3+25X^2-72X+144 ....ANSWER](https://image.slidesharecdn.com/adegree4polynomialwithintegercoefficientshaszerosand4-wit-230202235132-e4ef7a36/85/A-degree-4-polynomial-with-integer-coefficients-has-zeros-and-4-wit-docx-1-320.jpg)
