Question

question 10
solve the following quadratic inequality: $x^{2}-11x + 28>0$
write your answer in interval notation.
note: use oo for $infty$ and u for union
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question 11
use your graphing calculator to solve the equation graphically for all real solutions $x^{3}-6x^{2}+7x + 4 = 0$
solutions: $x=$
make sure your answers are accurate to at least two decimals
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Explanation:

Step1: Factor the quadratic expression

Factor $x^{2}-11x + 28$ to get $(x - 4)(x - 7)>0$.

Step2: Find the roots of the corresponding quadratic equation

Set $(x - 4)(x - 7)=0$. The roots are $x = 4$ and $x = 7$.

Step3: Test the intervals

Test the intervals $(-\infty,4)$, $(4,7)$ and $(7,\infty)$.
For $x<4$, let $x = 3$, then $(3 - 4)(3 - 7)=(-1)\times(-4)=4>0$.
For $4For $x>7$, let $x = 8$, then $(8 - 4)(8 - 7)=4\times1 = 4>0$.

Answer:

$(-\infty,4)\cup(7,\infty)$