I have to find a possible equation for which the following is true: [MATH]f(5)=0[/MATH], [MATH]f(-\sqrt{-2})=0[/MATH], there is a point of inflection at (2,0) and f(X) has a y intercept of 6.
My answer is [MATH]f(X)=(x-5)(x-2)^5(x+i\sqrt{2})[/MATH].
The given answer is [MATH]f(X)=(x-5)(x-2)^5(x^2+2)[/MATH], where the factor with complex roots has been transformed to have a degree of 2. In this case [MATH]x= +/- \sqrt{-2}[/MATH] where x is both positive and negative. In my answer [MATH]x=-\sqrt{-2}[/MATH], where x is the negative value (as stated in the question).
Is the given answer wrong, or am I wrong? And could you explain why? Thank you so much!
My answer is [MATH]f(X)=(x-5)(x-2)^5(x+i\sqrt{2})[/MATH].
The given answer is [MATH]f(X)=(x-5)(x-2)^5(x^2+2)[/MATH], where the factor with complex roots has been transformed to have a degree of 2. In this case [MATH]x= +/- \sqrt{-2}[/MATH] where x is both positive and negative. In my answer [MATH]x=-\sqrt{-2}[/MATH], where x is the negative value (as stated in the question).
Is the given answer wrong, or am I wrong? And could you explain why? Thank you so much!