Question

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

Answer 1

how should i start

Answer 2

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

Answer 3

D=b^2-4ac

Answer 4

So what I'm saying is:
\[Ax^2+Bx+C=0 => \text{ discriminant } = B^2-4AC\]
And we want here for the discriminant=0

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

Yep! :)

Answer 12

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

Answer 13

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

Answer 14

ok wait

Answer 15

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

Answer 16

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

Answer 17

yeah -28a

Answer 18

a^2-14a+53=0

Answer 19

is it right

Answer 20

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

Answer 21

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

Answer 22

a^2-14a+45=0

Answer 23

yep
do you know how to factor?

Answer 24

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

Answer 25

The quadratic formula?
That is fine. :)

Answer 26

yes

Answer 27

I solved it by factors..

Answer 28

thnx @myininaya U are great. Nice help

Answer 29

thanks

Answer 30

got 2 values 9 and 5 of a

Answer 31

Great! You go guys! :)

Answer 32

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.

Answer 33

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

Answer 34

How did it came.

Answer 35

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

Answer 36

\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \text{ is called the quadratic formual } \]
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.

Answer 37

So to slove the equation should i find a b c

Answer 38

*solve