How many integers satisfy the inequality x(3x-4) is less than or equal to 6x^2-3x+5/10

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- Oct 29th 2013, 06:04 AMvegasgunnerQuadratic inequality
How many integers satisfy the inequality x(3x-4) is less than or equal to 6x^2-3x+5/10

- Oct 29th 2013, 07:51 AMemakarovRe: Quadratic inequality
Why write 5/10 instead of 1/2 or 0.5?

- Oct 29th 2013, 08:13 AMHallsofIvyRe: Quadratic inequality
Perhaps you mean (6x^2- 3x+ 5)/10? Saying that $\displaystyle x(3x- 4)\le (6x^2- 3x+ 5)/10$ is the same as saying $\displaystyle 10x(3x- 4)\le 6x^2- 3x+ 5$ which in turn is the same as $\displaystyle 30x^2- 40x- (6x^2- 3x+ 5)= 24x^2- 37x- 5\le 0$. 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 $\displaystyle 24x^2- 37x- 5$. - Oct 29th 2013, 08:36 AMPlatoRe: Quadratic inequality
You might note that $\displaystyle 24x^2- 37x- 5=(8x+1)(3x-5)$

- Oct 29th 2013, 08:59 AMHallsofIvyRe: Quadratic inequality