if x+2 is factor of x3 + ax2 + 11x +6
find thr value of a
Answers
Given :- x + 2 a factor of x³ + ax² + 11x + 6
equating x + 2 with 0
➡ x + 2 = 0
➡ x = -2
we know that remainder is 0 when any polynomial is divided by it's factor.
therefore p(-2) = (-2)³ + a(-2)² + 11(-2) + 6 = 0
➡ -8 + 4a - 22 + 6 = 0
➡ -8 - 22 + 6 + 4a = 0
➡ -24 + 4a = 0
➡ 4a = 24
➡ a = 24/4
➡ a = 6
verification :-
= -24 + 4(6)
= -24 + 24
= 0
hence, the value of a is 6
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Step-by-step explanation:
given :- x + 2 a factor of x³ + ax² + 11x + 6
equating x + 2 with 0
➡ x + 2 = 0
➡ x = -2
we know that remainder is 0 when any polynomial is divided by it's factor.
therefore p(-2) = (-2)³ + a(-2)² + 11(-2) + 6 = 0
➡ -8 + 4a - 22 + 6 = 0
➡ -8 - 22 + 6 + 4a = 0
➡ -24 + 4a = 0
➡ 4a = 24
➡ a = 24/4
➡ a = 6
verification :-
= -24 + 4(6)
= -24 + 24
= 0
hence, the value of a is 6