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For how many integer values of x is $5x^{2}+19x+16 > 20$ not satisfied?

 Jun 28, 2023
 #1
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Solving the quadratic inequality, we get x > -1/2, x < -5/2.  So the inequality is not satisfied for x = -1 and x = -2.  The answer is 2.

 Jun 28, 2023
 #2
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To find the number of integer values of x for which the inequality $5x^{2}+19x+16 > 20$ is not satisfied, we can start by simplifying the inequality:

$5x^{2}+19x+16 > 20$

$5x^{2}+19x-4 > 0$

Now, we can solve this inequality by finding the values of x that make the quadratic expression positive.

To solve the inequality, we can factorize the quadratic expression:

$5x^{2}+19x-4 = (5x-1)(x+4)$

We need to find the values of x for which the product $(5x-1)(x+4)$ is greater than zero.

For this inequality to be satisfied, either both factors must be positive or both factors must be negative.

 Jun 29, 2023

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