Find approximate root
x^2-8x-12 between x=9 and x=10

Question

Find approximate root 
x^2-8x-12 between x=9 and x=10

amistre64 · Answer

simple enough with the quadratic formula

anonymous · Answer

Is it alright if you show me step by step on how to do it and what numbers go where? please.

amistre64 · Answer

when given the structure:$$ax^2+bx+c$$we can find the roots simple enough by using the formula:$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$or by completing the square

anonymous · Answer

So would my answer be -2,6. I did completing the square, but I dont understand when they mean between 9 and 10

amistre64 · Answer

most likely there are 2 roots and they want the one that is between 9 and 10

amistre64 · Answer

x^2-8x-12  ; 8/2 = 4; 4^2 = 16

x^2-8x+16 -16 -12 = 0

(x-4)^2 -28 = 0

x-4 = sqrt(28)

x = 4 + sqrt(28)

amistre64 · Answer

28 is close to 25

sqrt(25) = 5 so this is a bit bigger than 9 overall

anonymous · Answer

I got 9.29. Is that correct

amistre64 · Answer

my calculator says the same thing

anonymous · Answer

okay thank you so much.

amistre64 · Answer

youre welcome

anonymous · Answer

you helped me a lot and I really appreciate it.