SOLUTION: Write a polynomial function with rational coefficients in standard form with the given zeroes.
note i = imaginary
x = square root of 2, -i
work so far:
(x-square root of
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Question 66344This question is from textbook Algebra 2
: Write a polynomial function with rational coefficients in standard form with the given zeroes.
note i = imaginary
x = square root of 2, -i
work so far:
(x-square root of 2)(x+i)
xsquared + ix - x(square root of 2) - i(square root of 2)
This question is from textbook Algebra 2
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Write a polynomial function with rational coefficients in standard form with the given zeroes.
note i = imaginary
x = square root of 2, -i
work so far:
(x-square root of 2)(x+i)
xsquared + ix - x(square root of 2) - i(square root of 2)
FACTORS ARE
1.SQRT(2)
AND ITS CONJUGATE
2.-SQRT(2)
SINCE THE COEFFICIENTS OF POLYNOMIAL ARE REAL.
3.-I
AND ITS CONJUGATE
4.+I
SINCE THE COEFFICIENTS OF POLYNOMIAL ARE REAL.SO EQN.IS
P(X)=0=[X-SQRT(2)][X+SQRT(2)][X+I][X-I]=[X^2-2][X^2+1]=X^4-X^2-2
HENCE
X^4-X^2-2=0 IS THE POLYNOMIAL
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