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Math Help - Quadratic inequality

  1. #1
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    Exclamation Quadratic inequality

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

    Why write 5/10 instead of 1/2 or 0.5?
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  3. #3
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    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.
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  4. #4
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    Re: Quadratic inequality

    You might note that 24x^2- 37x- 5=(8x+1)(3x-5)
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  5. #5
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    Re: Quadratic inequality

    Quote Originally Posted by Plato View Post
    You might note that 24x^2- 37x- 5=(8x+1)(3x-5)
    Remarkable!
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