If x = 2 + 5i, then value of the expression x3 - 5x2 + 33x - 49 equals

Question

If x = 2 + 5i, then value of the expression x3 - 5x2 + 33x - 49 equals (A) -20 (B) 10 (C) 20 (D) -29

Tardigrade Admin · Accepted Answer

Given x = 2 + 5i <bR> ⇒ x - 2 = 5i ...(i) ⇒ x2 - 4x + 29 = 0 (squaring (i) both sides) Now, x3 - 5x2 + 33x - 49 = x (x2 - 4x + 29) - 1 ( x2 - 4x + 29) - 20 = x(0) - 1(0) - 20 = - 20

Q. If $x = 2 + 5 i$ , then value of the expression $x^{3} - 5 x^{2} + 33 x - 49$ equals

$- 20$

$10$

$20$

$- 29$

Given $x = 2 + 5 i$
$\Rightarrow x - 2 = 5 i ... (i)$
$\Rightarrow x^{2} - 4 x + 29 = 0$ (squaring (i) both sides)
Now, $x^{3} - 5 x^{2} + 33 x - 49$
$= x (x^{2} - 4 x + 29) - 1 (x^{2} - 4 x + 29) - 20$
$= x (0) - 1 (0) - 20 = - 20$

Q. If x=2+5i, then value of the expression x3−5x2+33x−49 equals

−20

10

20

−29