Question

what is the smallest integral value of n for which n³ + 7n² + 50n - 336 > 0
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Answer 1

Step-by-step explanation:

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Answer 2

Question :

What is the smallest integral value of n for which n³ + 7n² + 50n - 336 > 0?

Answer :

The smallest integral value of n for which n³ + 7n² + 50n - 336 > 0 is 4.

Given :

The polynomial n³ + 7n² + 50n - 336

To find :

The smallest integral value of n for which the given polynomial is greater than 0

Solution :

The given polynomial is n³ + 7n² + 50n - 336 > 0

When n = 1

n³ + 7n² + 50n - 336 = 1 + 7 + 50 - 336 = -278 which is less than 0

When n = 2

n³ + 7n² + 50n - 336 = 8 + 28 + 100 - 336 = 136 - 336

= - 200 which is less than 0

When n = 3

n³ + 7n² + 50n - 336 = 27 + 63 + 150 - 336 = - 96 which is yet less than 0

When n = 4

n³ + 7n² + 50n - 336 = 64 + 112 + 200 - 336 = 40 which is positive or greater than 0

Hence, the smallest integral value of n for which n³ + 7n² + 50n - 336 > 0 is 4.

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