If the bi-quadratic equation f ( x ) = x 4 + 2 x 3 - 16 x 2 - 22 x + 7 = 0 has 2 + 3 as one of its roots, then which of the following is not a root of f x ?

Step-by-step solution

Given, f ( x ) = x 4 + 2 x 3 - 16 x 2 - 22 x + 7 = 0 ∵   2 + 3 is one of the roots of f x = 0 ∴   2 - 3 is also one of the roots of f x = 0 Let us assume the other two roots of the f x = 0 are α ,   β ⇒ Sum of roots = - 2 ⇒ α + β + 2 + 3 + 2 - 3 = - 2 ⇒ α + β = - 6   … i And product of roots = 7 ⇒ α β 2 + 3 2 - 3 = 7 ⇒ α β = 7   … ii Put β = 7 α in equation i , we get ⇒ &#