Function g(x)

[alyren]

if G(x) = 24x^2 -24 and h(x) =55x, solve g(x)>h(x)

so far i set 1 side= 0, 24x^2 -55x+24>0, then i try factor. i think I'm doing this wrong

 

[mmm4444bot]

g(x) = 24x^2 - 24

h(x) = 55x

solve g(x) > h(x)

24x^2 - 55x + 24 > 0 The left side is wrong.

24x^2 - 55x - 24 > 0

then i try factor Yes, factoring could be the next step.

What factorization do you get?

There's more than one method, to solve this inequality.

If you're looking at factors, then take cases. Both factors must have the same sign, in order for their product to be positive.

Or, you can find x at the intersection points, and then use test values or a graph, to determine the solution intervals.

 

[alyren]

i can't factor the equation out by using factor formula, so i use the quadratic formula and i ended up getting 55±[(?2904)/48]. is this right?

 

[BigGlenntheHeavy]

$\displaystyle G(x) \ = \ 24x^2-24, \ H(x) \ = \ 55x$

$\displaystyle G(x) \ > \ H(x) \ \implies \ 24x^2-24 \ > \ 55x, \ \implies \ 24x^2-55x-24 \ > \ 0, \ (3x-8)(8x+3) \ > \ 0.$

$\displaystyle Now, \ inequalities \ are \ a \ little \ tricky, \ so \ let \ 3x-8 \ = \ 0, \ implies \ x \ = \ 8/3 \ and$

$\displaystyle let \ 8x+3 \ = \ 0, \ \implies \ x \ = \ -3/8.$

$\displaystyle --------------0+++++++++++++++++++++++++++++++++++++$

$\displaystyle --------------------------------0++++++++++++++++++++++++$

$\displaystyle Hence \ x \ < \ -3/8 \ and \ x \ >8/3 \ or \ (-\infty,-3/8)U(8/3,\infty)$

 

[mmm4444bot]

i can't factor the equation out by using factor formula

(The polynomial factors by grouping.)

so i use the quadratic formula and i ended up getting 55 ± [(?2904)/48]

Your 55 should be 55/48.

Your ?2904 should be ?5329.

$\displaystyle \frac{55 \pm \sqrt{(-55)^2 - 4(24)(-24)}}{2(24)}$

$\displaystyle \frac{55 \pm \sqrt{5329}}{48}$

$\displaystyle \frac{55 \pm 73}{48}$

$\displaystyle \frac{55 + 73}{48} = \frac{128}{48} = \frac{8}{3}$

$\displaystyle \frac{55 - 73}{48} = \frac{-18}{48} = -\frac{3}{8}$

These two solutions for x divide the Real number line into three intervals:

(-?, -3/8)

(-3/8, 8/3)

(8/3, ?)

Pick a test value of x, in each of these intervals, and use it to evaluate both g(x) and h(x) to discover in which interval(s) function g is greater than function h.