Answer:
[tex]x^{3} - (\sqrt{7} - 1)x^{2} - (2 + \sqrt{7} )x + 2\sqrt{7} = 0[/tex]
Step-by-step explanation:
We have to find the equation of a polynomial whose roots are - 2, 1 and √7.
It will be a single variable three-degree equation.
Let the variable is x.
So, (x + 2), (x - 1) and (x - √7) will be the factors of the equation.
Therefore, the equation can be written as
[tex](x + 2)(x - 1)(x - \sqrt{7} ) = 0[/tex]
⇒ [tex](x^{2} + x - 2)(x - \sqrt{7} ) = 0[/tex]
⇒ [tex](x^{3} + x^{2} - 2x - \sqrt{7} x^{2} - \sqrt{7} x + 2\sqrt{7} ) = 0[/tex]
⇒ [tex]x^{3} - (\sqrt{7} - 1)x^{2} - (2 + \sqrt{7} )x + 2\sqrt{7} = 0[/tex]
So, this is the required equation. (Answer)
