anonymous
  • anonymous
If the equation x^2+(7+a)x+7a+1=0 has equal roots,find the value of a. . . . ANSWER = {9,5}
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
how should i start
myininaya
  • myininaya
For a root with multiplicity two you need to need to have the discriminant equal to 0.
anonymous
  • anonymous
D=b^2-4ac

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More answers

myininaya
  • myininaya
So what I'm saying is: \[Ax^2+Bx+C=0 => \text{ discriminant } = B^2-4AC\] And we want here for the discriminant=0
anonymous
  • anonymous
but what is b and a and c the equation is a bit confusing
myininaya
  • myininaya
Since we want root with multiplicity 2 :) So \[B^2-4AC=0\]
myininaya
  • myininaya
\[\text{ you have } x^2+(7+a)x+(7a+1)=0\]
myininaya
  • myininaya
A is the number in front of x^2 B is the number in front of x C is the leftover part
anonymous
  • anonymous
\[x^2+(7+a)x+7a+1=0\]
anonymous
  • anonymous
A=1 B=(7+a) c=(7a+1)
myininaya
  • myininaya
Yep! :)
myininaya
  • myininaya
\[(7+a)^2-4(1)(7a+1)=0\]
myininaya
  • myininaya
That is B^2-4AC=0 You think you can solve that reply above for a?
anonymous
  • anonymous
ok wait
anonymous
  • anonymous
49+14a+a^2-14a+4=0
myininaya
  • myininaya
I think you mean -28a since -4(7)=-28 not -14
anonymous
  • anonymous
yeah -28a
anonymous
  • anonymous
a^2-14a+53=0
anonymous
  • anonymous
is it right
myininaya
  • myininaya
well .... I think your 53 is a little off. you have 49-4 you forgot to distribute that - earlier
myininaya
  • myininaya
\[49+14a+a^2-4(7a+1)=0\] \[49+14a+a^2-28a-4=0\] Now try combining like terms.
anonymous
  • anonymous
a^2-14a+45=0
myininaya
  • myininaya
yep do you know how to factor?
anonymous
  • anonymous
yep but i am solving this with quadratic is it ok?
myininaya
  • myininaya
The quadratic formula? That is fine. :)
anonymous
  • anonymous
yes
anonymous
  • anonymous
I solved it by factors..
anonymous
  • anonymous
thnx @myininaya U are great. Nice help
anonymous
  • anonymous
thanks
anonymous
  • anonymous
got 2 values 9 and 5 of a
myininaya
  • myininaya
Great! You go guys! :)
myininaya
  • myininaya
If you guys didn't understand why I set the discriminant equal to 0, then I will try to explain as best as possible. If discriminant is equal to 0, then you will have on root (multiplicity 2) If discriminant is equal to negative number, you have two imaginary solutions If discriminant is equal to positive number, you have two real solutions.
myininaya
  • myininaya
The discriminant is \[B^2-4AC \]
anonymous
  • anonymous
How did it came.
anonymous
  • anonymous
@myininaya how to solve the equation to get the discriminant..
myininaya
  • myininaya
\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \text{ is called the quadratic formual } \] The discriminant is that thing under the radical It is what determines if you have one root (w/ multiplicity 2) , imaginary roots, or real roots.
anonymous
  • anonymous
So to slove the equation should i find a b c
anonymous
  • anonymous
*solve

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