# Quadratic inequality

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• October 29th 2013, 06:04 AM
vegasgunner
Quadratic inequality
How many integers satisfy the inequality x(3x-4) is less than or equal to 6x^2-3x+5/10
• October 29th 2013, 07:51 AM
emakarov
Re: Quadratic inequality
Why write 5/10 instead of 1/2 or 0.5?
• October 29th 2013, 08:13 AM
HallsofIvy
Re: Quadratic inequality
Perhaps you mean (6x^2- 3x+ 5)/10? Saying that $x(3x- 4)\le (6x^2- 3x+ 5)/10$ is the same as saying $10x(3x- 4)\le 6x^2- 3x+ 5$ which in turn is the same as $30x^2- 40x- (6x^2- 3x+ 5)= 24x^2- 37x- 5\le 0$. You can use the quadratic formula to determine where that polynoial is equal to 0. It will be less than 0 between those two values so it is only necessary to determine how many integers there are between the two roots of $24x^2- 37x- 5$.
• October 29th 2013, 08:36 AM
Plato
Re: Quadratic inequality
You might note that $24x^2- 37x- 5=(8x+1)(3x-5)$
• October 29th 2013, 08:59 AM
HallsofIvy
Re: Quadratic inequality
Quote:

Originally Posted by Plato
You might note that $24x^2- 37x- 5=(8x+1)(3x-5)$

Remarkable!