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Question :–
• If x + k is a factor of the polynomial x³ + kx² - 2x + k + 5 = 0 , then k =
(a) ⅗
(b) - ⅗
(c) - 5/3
(d) 5/3
ANSWER :–
GIVEN :–
• x + k is a factor of the polynomial x³ + kx² - 2x + k + 5 = 0.
TO FIND :–
• Value of 'k' = ?
SOLUTION :–
• Zero of factor will satisfy the polynomial. So that x = - k will satisfy the polynomial.
=> (-k)³ + k(-k)² - 2 (-k) + k + 5= 0
=> - k³ + k (k²) + 2k + k + 5 = 0
=> -k³ + k³ + 3k + 5 = 0
=> 3k + 5 = 0
=> 3k = -5
=> k = -(5/3)
▪︎ Hence , Option (c) is correct.
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