If the equation x^2+(7+a)x+7a+1=0 has equal roots,find the value of a.
.
.
.
ANSWER = {9,5}

- anonymous

If the equation x^2+(7+a)x+7a+1=0 has equal roots,find the value of a.
.
.
.
ANSWER = {9,5}

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- anonymous

how should i start

- myininaya

For a root with multiplicity two you need to need to have the discriminant equal to 0.

- anonymous

D=b^2-4ac

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## More answers

- 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

but what is b and a and c the equation is a bit confusing

- myininaya

Since we want root with multiplicity 2 :)
So \[B^2-4AC=0\]

- myininaya

\[\text{ you have } x^2+(7+a)x+(7a+1)=0\]

- myininaya

A is the number in front of x^2
B is the number in front of x
C is the leftover part

- anonymous

\[x^2+(7+a)x+7a+1=0\]

- anonymous

A=1
B=(7+a)
c=(7a+1)

- myininaya

Yep! :)

- myininaya

\[(7+a)^2-4(1)(7a+1)=0\]

- myininaya

That is B^2-4AC=0
You think you can solve that reply above for a?

- anonymous

ok wait

- anonymous

49+14a+a^2-14a+4=0

- myininaya

I think you mean -28a since -4(7)=-28 not -14

- anonymous

yeah -28a

- anonymous

a^2-14a+53=0

- anonymous

is it right

- myininaya

well .... I think your 53 is a little off.
you have 49-4
you forgot to distribute that - earlier

- myininaya

\[49+14a+a^2-4(7a+1)=0\]
\[49+14a+a^2-28a-4=0\]
Now try combining like terms.

- anonymous

a^2-14a+45=0

- myininaya

yep
do you know how to factor?

- anonymous

yep but i am solving this with quadratic is it ok?

- myininaya

The quadratic formula?
That is fine. :)

- anonymous

yes

- anonymous

I solved it by factors..

- anonymous

thnx @myininaya U are great. Nice help

- anonymous

thanks

- anonymous

got 2 values 9 and 5 of a

- myininaya

Great! You go guys! :)

- 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

The discriminant is \[B^2-4AC \]

- anonymous

How did it came.

- anonymous

@myininaya how to solve the equation to get the discriminant..

- 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

So to slove the equation should i find a b c

- anonymous

*solve

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