what is the anzwer for 11x+12>5x^2

Question

11x+12>5x^2

11x-11x+12>5x^2-11

12>5x^2-11x

i cant figure out the rest :(

sorry...

Answer 1

Hi, Sea,

 

I would first start by moving all of the terms to one side of the inequality, then we will treat it like any other quadratic equation

 

    11x + 12 > 5x²

 

Subtracting the 11x and 12 from both sides:

 

    0 > 5x² - 11x - 12

 

The quadratic expression (5x² - 11x -12), plotted, would be a parabola, opening upward.  We need to identify what range of x values would make the expression be less than 0.

 

We can solve for the zeroes (roots) of the quadratic, either using the quadratic equation, or by completing the square. I much prefer the quadratic equation, so I'll use that.

 

The zeroes of the quadratic are -b +/- √(b² - 4ac)

                                                       2a

 

    -(-11) +/- √(-11² - 4 (5) (-12))

                     2(5)

 

    11 +/- √(361)

            10

 

    11 +/- 19

        10

 

    30/10     or         -8/10

 

    3            or        -4/5

 

Since those are the x-values that make the expression equal to 0, and the expression is an upward-opening parabola, the x-values between those two zeroes would make the expression less than 0.

 

So, -4/5 < x < 3

Answer 2

11x + 12 > 5x²

-5x² + 11x + 12 > 0

 

Graphically, the equation y = -5x² + 11x + 12 is a down-facing parabola with y-intercept of 12. To find the x-intercepts, let's factor:

 

(-5x -4) (x - 3) > 0

 

Set each factor on the left equal to zero:

-5x - 4 = 0

-5x = 4

x = -5/4

 

x - 3 = 0

x = 3

 

So the graph crosses the x-axis at -5/4 and 3. y is greater than zero for values of x between -5/4 and 3, and thus the solution to the inequality is:

 

-5/4 < x < 3