anonymous
  • anonymous
finding zeros : f(x)=49x^2-144 how will i solve this one?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
what can you tell about the numbers 49 and 144...?
anonymous
  • anonymous
perfect squares?
campbell_st
  • campbell_st
yep... so give you have 49x^2 this is the difference of 2 squares... thats why theres a subtraction sign this may help you factorise \[(ax +b)(ax - b)=a^2x^2 - b^2\] after factoring let it equal zero... then solve for x

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anonymous
  • anonymous
are there any shortcuts on how to solve it?
campbell_st
  • campbell_st
well you know 49 and 144 are square number.... so what do you think a and b might be...?
anonymous
  • anonymous
7 and 12
anonymous
  • anonymous
or is it 7x+12 7x-12 ??
campbell_st
  • campbell_st
thats it so you are solving (7x - 12)(7x + 12) = 0 so really you just need to solve 7x - 12 = 0 and 7x + 12 = 0 hope it makes sense
anonymous
  • anonymous
so the roots are -7 and 12???
campbell_st
  • campbell_st
no, you need to solve 7x - 12 = 0 then its 7x = 12 x = 12/7 thats one solution. You need to do the other 7x + 12 = 0
anonymous
  • anonymous
oohhhh
campbell_st
  • campbell_st
the solutions are the roots
anonymous
  • anonymous
7x=-12 x= -12/7
anonymous
  • anonymous
oh okay i understand it now thanks a lot... i have other problem here help me again please.. f(d)=2d^2-10d
anonymous
  • anonymous
i don't know how to solve it because it's not a perfect square number
skullpatrol
  • skullpatrol
Do you see a common factor?
anonymous
  • anonymous
2?
skullpatrol
  • skullpatrol
Yes, there is another one.
campbell_st
  • campbell_st
glad to help... lots of good people here to help with the next question
anonymous
  • anonymous
2 and 2d?
nirmalnema
  • nirmalnema
u can use a identity here a^2-b^2=(a+b)(a-b)
skullpatrol
  • skullpatrol
$$\huge 2d^2-10d= 2d(d - 5)$$
anonymous
  • anonymous
But where's the other squared number?
anonymous
  • anonymous
I don't understand it :(
nirmalnema
  • nirmalnema
49x^2-144 can be written as (7x+12)(7x-12) so x =12/7 and -12/7
nirmalnema
  • nirmalnema
these are the two roots
anonymous
  • anonymous
f(d)=2d^2-10d
anonymous
  • anonymous
That question was answered already @nirmalnema
anonymous
  • anonymous
Do you know how to do it now @MCath?
nirmalnema
  • nirmalnema
ohh...ok
anonymous
  • anonymous
i don't know this one f(d)=2d^2-10d
skullpatrol
  • skullpatrol
|dw:1377768008759:dw|
anonymous
  • anonymous
haaa?
skullpatrol
  • skullpatrol
|dw:1377768116175:dw|
nirmalnema
  • nirmalnema
2d(d-5)=0 d=5
anonymous
  • anonymous
can i just divide them into 2d?
anonymous
  • anonymous
|dw:1377768212960:dw|
skullpatrol
  • skullpatrol
|dw:1377768241316:dw|
skullpatrol
  • skullpatrol
This is called the "zero product property." For all real numbers a and b, ab=0 if and only if a=0 or b=0.
skullpatrol
  • skullpatrol
Recall that zero times any number is zero.
anonymous
  • anonymous
so the roots are 0 and 5?
skullpatrol
  • skullpatrol
Correct.
anonymous
  • anonymous
but i don't know how did i got 5
skullpatrol
  • skullpatrol
$$\Huge2d =0$$ $$\huge or$$ $$\huge d - 5 = 0$$
anonymous
  • anonymous
ooooowwwwww yess I knew it!! I just didn't had the confidence to solve it hehe Thanks a lot :D
skullpatrol
  • skullpatrol
You should be extremely confident with the result that 0 times any number is 0.
skullpatrol
  • skullpatrol
It is also the reason you can not divide by 0.
anonymous
  • anonymous
then why the -5 is 5 ???
skullpatrol
  • skullpatrol
|dw:1377769087904:dw|
skullpatrol
  • skullpatrol
|dw:1377769591320:dw|
anonymous
  • anonymous
Thank you so much
skullpatrol
  • skullpatrol
Thank you for trying to learn something new in mathematics.
anonymous
  • anonymous
thank you for the patience hehe

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