r^2+10r-23=0
I used the quadratic formula and I got a -5+2√12
However the real answer is -5+4√3
What am I doing wrong?
A survey of 100 people to determine their preferred source of information gave the following results:
65 watched television
39 read the newspaper
39 listened to the radio
20 watched television and read the newspaper
27 watched television and listened to the radio
9 read the newspaper and listened to the radio
6 watched television, read the newspaper and listened to the radio
a) How many people surveyed used another means of communication other than the three listed?
b) How many people surveyed used only one of the three methods of communication?
You got the right answer! It just needed to be reduced.
-5 + 2*�ã(12)
=-5+2*�ã(4*3)
=-5+2*�ã4 * �ã3
=-5+2*2*�ã3
=-5+4*�ã3
My Alt+251 keyboard did not post as a square root--reposting...
-5+2*SQR(12)
=-5+2*SQR(4*3)
=-5+2*SQR(4)*SQR(3)
=-5+2*2*SQR(3)
=-5+4*SQR(3)
To solve the quadratic equation r^2 + 10r - 23 = 0, you correctly used the quadratic formula. The quadratic formula is given by:
r = (-b ± √(b^2 - 4ac))/(2a)
In this equation, a = 1, b = 10, and c = -23.
Substituting these values into the formula, we get:
r = (-10 ± √(10^2 - 4(1)(-23)))/(2(1))
Simplifying further:
r = (-10 ± √(100 + 92))/(2)
r = (-10 ± √(192))/(2)
r = (-10 ± √(64*3))/(2)
r = (-10 ± 8√3)/(2)
Notice that you can simplify the square root of 64 as 8, not 2√12. This is because 64 = 8^2. So, the correct simplification is:
r = (-10 ± 8√3)/(2)
Simplifying further:
r = -5 ± 4√3
Therefore, the two possible solutions are:
r = -5 + 4√3
r = -5 - 4√3
Therefore, your initial calculations were incorrect. You mistakenly simplified √(64*3) as 2√12 instead of 8√3.