Question

Please solve it as fast as possible with explanation.​

Answer 1

Answer:

k = -4

h = 1

Step-by-step explanation:

f(x) = x³ + kx² + hx + 6

according to factor theorem, for f(x) to be a factor of both (x+1) and (x-2), f(-1) and f(2) = 0

=> f(-1) = (-1)³ + k(-1)² +h(-1) + 6 = 0

=> -1 + k - h + 6 = 0

=> k + 5 - h = 0

and f(2) = (2)³ + k(2)² + h(2) + 6 = 0

=> 8 + 4k + 2h + 6 = 0

=> 4k + 14 + 2h = 0

=> 2k + 7 + h = 0

adding both equations, 3k + 12 = 0

=> k = -4

=> h = -4 + 5 = 1

Answer 2

$\huge{\mathfrak{\red{Answer}}}$

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$\huge{\boxed{\red{K\:=\:-4}}}$

$\huge{\boxed{\red{H\:=\:1}}}$

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➤ Solution :

f (x) = x³ + kx² + hx + 6

according to the factor theorem, for f (x) to be a factor of both ( x + 1 ) and ( x - 2 ) , f (-1) and f (2) = 0

➜ f (-1) = (-1)³ + k (-1) ² + h (-1) + 6 = 0

➜ -1 + k - h + 6 = 0

➜ k + 5 - h = 0

and f (2) = (2)³ + k (2)² + h (2) + 6 = 0

➜ 8 + 4k + 2h + 6 = 0

➜ 4k + 14 + 2h = 0

➜ 2k + 7 + h = 0

adding both equations , 3k + 12 = 0

➜ k = -4

➜ h = -4 + 5 = 1

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