careless850
If someone could help me with these last few problems, it would be nice. Check all polynomials that are perfect square trinomials:
A) 49x^2 − 8x + 16
B) 4a^2 − 20a + 25
C) 25b^2 − 5b + 10
D) 16x^2 − 8x + 1
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careless850
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Anyone? :)
careless850
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Which ones are perfect square trinomials?
megan1124
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a is do you know how i figured that out?
careless850
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No, I don't.
megan1124
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have you learned foil?
Diyadiya
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No A is not the right answer!
careless850
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Diya, there is more than one I can choose for the right answer. How come A isn't one of them?
megan1124
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|dw:1338062447129:dw| that is y it is
Diyadiya
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If \( ax^2+bx+c \) is a perfect square trinomial then the discriminant will be zero.
Do you know to find the discriminant?
\( D= b^2- 4ac =0\)
careless850
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I'm so confused...
megan1124
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thats not how you do that
Diyadiya
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@megan1124 (7x-4)(7x-4) = 49x^2-56x+16
megan1124
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noo it equals a
careless850
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um.. Can someone just show me how to do these or.. if you are going to argue.. just give me a hint to the right answers please...
megan1124
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are you in algebra 1?
careless850
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Yep
careless850
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for the 3rd time.
Diyadiya
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@careless850
Lets check the second option
\( 4a^2 − 20a + 25 \) this is of the form \( ax^2+ bx + c \)
Now find \(b^2-4ac \)
\(b^2-4ac = (-20)^2- 4*4*25= 400-400 = 0 \)
Now verify if your answer is right
\( 4a^2 − 20a + 25 = (5-2a)(5-2a) =(5-2a)^2 \)
megan1124
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ok thanks its and b :) because you can divide the first one and last one by a number and get the same number you divided by and get a whole number
careless850
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O.o what? So is one of the answers A or is one B?
megan1124
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the 2 answers are a and b because if you factor them you don't get more that 2 numbers like the one i showed you above earlier
careless850
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So C and D aren't?
Diyadiya
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\( 49x^2 − 8x + 16 \)
Find \(b^2 -4ac \)
b=-8 , a=49 , c=16
\(b^2 -4ac = (-8)^2 - 4(49)(16) = -3120 \)
So option A is not the right answer
Can you check for C now?
careless850
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Diya, A isn't right? So the only right answer is B?
Diyadiya
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A isn't Right! i just showed you why..
B is right
But you have to check the others too
megan1124
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you can have more than one right answer right? if so its a and b
Diyadiya
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@megan1124 A is not the right answer
Can you tell me what is (7x-4)(7x-4) ??
megan1124
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its a
Diyadiya
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Nope, try to solve it and see
careless850
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There is multiple answers that can be right.
Diyadiya
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Can you find the discriminant of C & D ?
\( D= b^2-4ac \)
careless850
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I don't know what the disciminant is.
Diyadiya
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\( 25b^2 − 5b + 10\) this is of the form \( ax^2 + bx +c \)
|dw:1338063436660:dw|
so
a =25
b=-5
c=10
Now find Dicriminant \( D =b^2-4*a*c\)
Can you do that?
Diyadiya
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Just plug in the values of a ,b & c in the equation \(b^2 - 4ac \)
can you ?
Diyadiya
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@careless850 Pls tell me if you're stuck somewhere
Diyadiya
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is it equal to zero or some other number ?
careless850
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I'm still confused..
Diyadiya
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where are you stuck ? did you find b^2 -4ac?
careless850
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No.
Diyadiya
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Find it :) & check if its equal to zero
careless850
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How do I find it?
careless850
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......
Diyadiya
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25b^2 − 5b + 10
Given :
a =25
b=-5
c=10
b^2 - 4ac
Diyadiya
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(-5)^2 - 4* 25 * 10
is it equal to zero?
careless850
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no
Diyadiya
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so its not a perfect square trinomial
Now do the last one
D) 16x^2 − 8x + 1
Can you tell me what is a ,b & c here?
careless850
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a is 16
Diyadiya
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yes
b & c?
careless850
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-8 is b and 1 is c.
Diyadiya
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Right!!!!!!!
Now Find the discriminant
How do you find it?
careless850
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So I would do this.. -> -8^2 -4*16*1.
Diyadiya
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Yessss good work :)
careless850
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how to solve that, I don't know, but that's the problem.. lol
Diyadiya
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\( (8)^2 - 4 \times 16 \times 1 \)
What is \( 8^2 \) ?
careless850
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64
careless850
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64-64 = 0
careless850
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So it's a PST
Diyadiya
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Yess!! so its a perfect square trinomial :)
You can verify by factoring ^_^
careless850
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I see. Pretty easy now I guess. So the only ones that are perfect square trinomials are B and D?
careless850
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Can you help me with another?
Diyadiya
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Yes, If you factorise 16x^2 − 8x + 1 you'll get (1-4x)(1-4x) = (1-4x)^2
Post it as a new question :)
Diyadiya
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Yes its B & D
careless850
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Thank you. :))
Diyadiya
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Np :)