Currently i just applying for some online degree courses, one of the subject is algebra and function. I need to study by myself only, so it's a bit difficult for me when the assignment given before any class started and need to submti in a short time period.
Meaning that may be the question from the assignment is on Topic 5 or Topic 9 but current the class not even start Topic 1.
By the way, here are some continue for the question.
Show that x^2-5x+11 > 0 for all the integers
is it meaning that need to subtitute the x with 1,2,3,4 in the equation , what ever number get the value >0 is countable ?
Complete the square...
$\displaystyle \displaystyle \begin{align*} x^2 - 5x + 11 &= x^2 - 5x + \left(-\frac{5}{2}\right)^2 - \left(-\frac{5}{2}\right)^2 + 11 \\ &= \left(x - \frac{5}{2}\right)^2 - \frac{25}{4} + \frac{44}{4} \\ &= \left(x - \frac{5}{2}\right)^2 + \frac{19}{4} \end{align*}$
Since $\displaystyle \displaystyle \left(x - \frac{5}{2}\right)^2 \geq 0$ for all $\displaystyle \displaystyle x$, then $\displaystyle \displaystyle \left(x - \frac{5}{2}\right)^2 + \frac{19}{4} > 0$ for all $\displaystyle \displaystyle x$.
Thank you for the reply.
Just a question, If based on Discriminant, when b^2-4ac is negative, so no real root, b^2 - 4ac < 0
How come we can use (x - 5/2)^2 + 19/4 > 0
2nd question, when we use the formula,
x= -b +- Sq root b^2-4ac / 2a
x= 5 + sq root.-19/2 , 5-sq. root-19/2
If based on the question, Show that x^2 - 5x + 11 > 0 for all integers x., i should use the answer from the formula or based on the answer from the completing the square ?