Question

f(x) is a cubic polynomial where the coefficient of x^3 is one. the roots of f(x) = 0 are -3, 1+sqrt2, 1-sqrt2. Express f(x) as a cubic polynomial in x with integer coefficients

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

The roots are given to be -3 , 1+$\sqrt{2}$ , and 1-$\sqrt{2}$ .

So ,

$x^{$= -3 ---> ($x^{}$+3) is a factor .

$x^{}$= 1+$\sqrt{2}$-----> ($x^{}$- (1+$\sqrt{2}$)) is a factor .

Similarly , ($x^{}$- ( 1-$\sqrt{2}$)) is also a factor

so , f($x^{}$) = ($x^{}$+3)($x^{}$- (1+$\sqrt{2}$))($x^{}$- ( 1-$\sqrt{2}$))

      f($x^{}$) = ($x^{}$+3)( $x^{2}$ -2$x^{}$-1)

      f($x^{}$)= $x^{3}$ - 2$x^{2}$-$x^{}$-3$x^{2}$+6$x^{}$+3

      f($x^{}$) = $x^{3}$-5$x^{2}$+5$x^{}$+3

Hope this helps.