HELP PLZ
how many real solutions does the equation have -8x^2-8x-2=0

Question

HELP PLZ
how many real solutions does the equation have -8x^2-8x-2=0

misty1212 · Answer

HI!!

misty1212 · Answer

shall we find them?  then we will know for sure !

anonymous · Answer

A: one solution
B:two solutions
c:no solutions
D: infinite

misty1212 · Answer

i would divide all by $-2$ so make life easier and start with 
$$4x^2+4x-1=0$$ then compute the discriminant or just use the quadratic formula which has the discriminant in it

misty1212 · Answer

also i made a mistake, it should be 
$$\huge 4x^2+4x+1=0$$

misty1212 · Answer

you might even recognize this as a perfect square, but even if you do not, you can compute 
$$b^2-4ac$$ with 
$$a=4,b=4,c=1$$

misty1212 · Answer

let me know what you get

anonymous · Answer

ok let me do the math real quick

misty1212 · Answer

yeah good "do the math" is pretty much what this is all about

anonymous · Answer

i got 4+- sqrt of 0/8

misty1212 · Answer

lol

anonymous · Answer

?...

misty1212 · Answer

$$b^2-4ac=4^2-16=0$$ so there is one solution

anonymous · Answer

oh ok i get it i put it over 4a cuz thats the quadratic formula

misty1212 · Answer

do not write $\sqrt0$  your math teacher will think you are a moron, just leave it as 
$$\frac{4}{8}=\frac{1}{2}$$

tkhunny · Answer

-8x^2-8x-2=0

Dividing by -2

4x^2 + 4x + 1 = 0

Immediately, there are NO positive Real Roots

Substituting -x

4x^2 - 4x + 1 = 0

There might be 2 negative Real Roots (Counting multiplicities)

Discriminant

$4^{2} - 4(4)1 = 16 - 16 = 0$  Aha!!  There are two negative roots and they are equal.

Sometimes, the spirit of the question does not require the solution.  Just answer the question.

misty1212 · Answer

in fact 
$$4x^2+4x+1=(2x+1)^2$$ and if 
$$(2x+1)^2=0$$ then the only solution is 
$$2x+1=0\
2x=-1\
x=-\frac{1}{2}$$

anonymous · Answer

so then there is 1 solution..

misty1212 · Answer

yes dear just one
be careful here

anonymous · Answer

ok thank you :) could u help me with another?

misty1212 · Answer

the quadratic formula is 
$$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$you dropped the minus sign

misty1212 · Answer

yes sure why not?

anonymous · Answer

what is the value of C so that x^2-11x+c is a perfect-square trinomial

misty1212 · Answer

what is half of 11?

misty1212 · Answer

use a fraction, not a decimal

tkhunny · Answer

There are two.  The fundamental premise of a quadratic equation is that it has TWO solutions.  Just because they happen to be equal, does not mean there is only one.

anonymous · Answer

A:121
B:121/4
c:-11/2
d:121/2
and halk of 11 is 5.5

anonymous · Answer

oh 11/2

misty1212 · Answer

rigth

misty1212 · Answer

now what is $\left(\frac{11}{2}\right)^2$?

anonymous · Answer

@tkhunny  you mean the first one? and @misty1212 30.25

misty1212 · Answer

lol stop with the decimals

misty1212 · Answer

you see any decimals in your answer? no, of course not
square the top, square the bottom

anonymous · Answer

30 1/4

misty1212 · Answer

grrr

misty1212 · Answer

fractions, not decimals
not mixed numbers 
just fractions

misty1212 · Answer

it is actually less work to do it with fractions  $$\frac{11}{2}\times \frac{11}{2}=?$$

anonymous · Answer

121/4

misty1212 · Answer

bingo

anonymous · Answer

thats the answer? cool, that was easy

anonymous · Answer

even though its a negative 11?

misty1212 · Answer

lol yes it certainly was wan't it? when you know what you are doing much of this is very easy
$$\color\magenta\heartsuit$$

misty1212 · Answer

when you square it, it is positive

anonymous · Answer

cool thanks :)

misty1212 · Answer

yw dear

anonymous · Answer

@misty1212 can you help me again?

misty1212 · Answer

yes, but post in a new thread it is hard to scroll down all the time