Question : If $x^{3} + 2 x^{2} - 5 x + k$ is divisible by $x + 1$ , then what is the value of $k$ ?
Option 1: –6
Option 2: –1
Option 3: 0
Option 4: 6

Question

Question : If $4 (2 x + 3) > 5 - x$ and $5 x - 3 (2 x - 7) > 3 x - 1,$ then $x$ can take which of the following values?

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Answer 1

Correct Answer: –6

Solution : Given: $f (x) = x^{3} + 2 x^{2} - 5 x + k = 0$ is divisible by $x + 1$ .
So, $x^{3} + 2 x^{2} - 5 x + k = 0$ when $x = - 1$
⇒ $(- 1)^{3} + 2 (- 1)^{2} - 5 (- 1) + k = 0$
⇒ $- 1 + 2 + 5 + k = 0$
⇒ $k = - 6$
Hence, the correct answer is –6.

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Question : If x3+2x2−5x+k is divisible by x+1, then what is the value of k?Option 1: –6Option 2: –1Option 3: 0Option 4: 6

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Question : If $x^{3} + 2 x^{2} - 5 x + k$ is divisible by $x + 1$ , then what is the value of $k$ ?
Option 1: –6
Option 2: –1
Option 3: 0
Option 4: 6