Medal if helped asap A quadratic equation is shown below: x2 + 5x + 4 = 0 Part A: Describe the solution(s) to the equation by just determining radicand. Show your work. (3 points) Part B: Solve 4x2 -12x + 5 = 0 using an appropriate method. Show the steps of your work, and explain why you chose the method used. (4 points) Part C: Solve 2x2 -10x + 3 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)
how do we define the radicand?
radicand, aka discriminant
discriminant: b^2 - 4ac
lets see how much the asker already knows before hand
ok
i dont really remember much about the radicand
the radicand is generally given as ... and study gurl has provided it
It is part of the quadratic formula: where \[ax^2+bx+c=0\] \[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
this should be ringing some bells from what you have studied. so the next question to get your mind rolling would be what a,b, and c refer to
o yeah i remember how to use that formula
radicand is another name for square roots, cube roots, etc. (basically any type of root). It is specifying the stuff inside the square root
i tend to prefer including the sqrt as part of the discriminant since it helps to see why the rules applied to it are as they are
ok
@SedateFrog712 Do you remember what the discriminant of a quadratic equation indicates about the solutions?
me too @amistre64
you dont have to use that formula can solve by factoring as well
KIO right, but the question is specific here.
Yes, you can @KlOwNlOvE , but the first question refers to the discriminant, which is part of the quadratic formula
tkind of @StudyGurl14
ahh didnt read over that part my apologies
good luck, youre in capable hands :)
If the discriminant is positive, there are two real roots. If it is zero, there is one real root (a double root). And if the discriminant is negative, there are two imaginary roots and no real roots
ok
So, do you know how to find the value of the discriminant? (Use the information given previously to help you!)
i would use the quadratic formula correct
discriminant: b^2 - 4ac
a=1 b=5 c=4
you mean a=2 @KlOwNlOvE
no, a =1
o ok
because it is x^2, so imagine the 1 in front of the x^2
If a=2, then it would be 2x^2
Okay, so if you have... \[b^2-4ac\] What does that equal?
(plug in the known values for a, b, and c)
5^2 - 4(1)(4) = 25 - 16= 9
Good job!
Okay, now refer back to what I said about discriminants. What does the 9 indicate about the solution of the equation?
"If the discriminant is positive, there are two real roots. If it is zero, there is one real root (a double root). And if the discriminant is negative, there are two imaginary roots and no real roots"
ok so 9 means there are two real roots
@StudyGurl14
and sqrt of 9 is?
81
no
3
square root of 9 not 9 squared
yes
uhh im stupid
ok so does that conclude a
i think so solutions 3 3 ready for part b?
yep
@StudyGurl14 im ready for part b
i didnt
nvm sorry i didn't read far enough ahead
okay, so yeah, part b
you can do this three ways. Graphng, using the quadratic formula, or factoring. which method do you choose?
would that be right? i haven't done this radicand things yet
would what be right?
the solutions be 33 or just 3?
the solutions would be two real roots. you don't know them yet. The descriminant doesn't tell you what the solutions are, just how many and if they are real or imaginary
and the discriminant is 9, not 3
which method would be easiest
graphing is easiest if you have access to an online graphing calc like desmos.com. But for this one, I recommend factoring
i find quadratic easier than the others
ok lets use factoring first
oops\[4x^2-12x+5=0\]
Oh oops i was looking at the wrong one (sorry!) for this one, quadratic fwould be easier
ok let do quadratic
i was looking at x^2+5x + 4, sorry. i didn't realize part 2 had a different equation
Quadratic equation \[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
\[ax^2+bx+c=0\] \[4x^2-12x+5=0\] a= ? b = ? c= ?
a=4 b=12 c=5
b is wrong
(don't forget the minus sign is included...)
|dw:1413247661965:dw|
Join our real-time social learning platform and learn together with your friends!