Find the equation given the roots -2, 1, and square root of 7

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)