Is 9 − 6 i 9 - 6 i 9 − 6 i a solution of the equation x 2 − 18 x + 117 = 0 ? x ^ { 2 } - 18 x + 117 = 0 ? x 2 − 18 x + 117 = 0 ? A) NoB) Yes

Question

Is   9 − 6 i 9 - 6 i 9 − 6 i   a solution of the equation   x 2 − 18 x + 117 = 0 ? x ^ { 2 } - 18 x + 117 = 0 ? x 2 − 18 x + 117 = 0 ? A) NoB) Yes

Simsons Tan Jia Hui · Accepted Answer

Final Answer : B, Explanation :   To check whether   9 − 6 i 9-6i 9 − 6 i   is a solution of the given equation or not, we substitute   x = 9 − 6 i x=9-6i x = 9 − 6 i   in the equation and simplify. x 2 − 18 x + 117 = ( 9 − 6 i ) 2 − 18 ( 9 − 6 i ) + 117 = ( 81 − 36 i 2 − 108 i ) + ( 117 − 108 i ) = ( 81 + 216 ) − ( 36 + 108 ) i = 297 − 144 i  x^2-18x+117 & =(9-6i)^2-18(9-6i)+117\ & =(81-36i^2-108i)+(117-108i)\ & =(81+216)-(36+108)i\ & =297-144i  x 2 − 18 x + 117 ​ = ( 9 − 6 i ) 2 − 18 ( 9 − 6 i ) + 117 = ( 81 − 36 i 2 − 108 i ) + ( 117 − 108 i ) = ( 81 + 216 ) − ( 36 + 108 ) i = 297 − 144 i ​ Since   297 − 144 i ≠ 0 297-144i
eq0 297 − 144 i  = 0  ,   9 − 6 i 9-6i 9 − 6 i   is not a solution of the equation. Therefore, the answer is B.

Is $9 - 6 i$ a solution of the equation $x ^ { 2 } - 18 x + 117 = 0 ?$

A) No
B) Yes

Definitions

Learning Objectives

Learning Objectives

Related questions

Is 9−6i9 - 6 i9−6i a solution of the equation x2−18x+117=0?x ^ { 2 } - 18 x + 117 = 0 ?x2−18x+117=0? A) NoB) Yes

Definitions

Learning Objectives

Learning Objectives

Related questions

Is $9 - 6 i$ a solution of the equation $x ^ { 2 } - 18 x + 117 = 0 ?$

A) No
B) Yes