koli123able 3 years ago If the equation x^2+(7+a)x+7a+1=0 has equal roots,find the value of a. . . . ANSWER = {9,5}

1. koli123able

how should i start

2. myininaya

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

3. koli123able

D=b^2-4ac

4. 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

5. koli123able

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

6. myininaya

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

7. myininaya

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

8. myininaya

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

9. koli123able

$x^2+(7+a)x+7a+1=0$

10. koli123able

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

11. myininaya

Yep! :)

12. myininaya

$(7+a)^2-4(1)(7a+1)=0$

13. myininaya

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

14. koli123able

ok wait

15. koli123able

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

16. myininaya

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

17. koli123able

yeah -28a

18. koli123able

a^2-14a+53=0

19. koli123able

is it right

20. myininaya

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

21. myininaya

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

22. koli123able

a^2-14a+45=0

23. myininaya

yep do you know how to factor?

24. koli123able

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

25. myininaya

The quadratic formula? That is fine. :)

26. koli123able

yes

27. Miyuru

I solved it by factors..

28. Miyuru

thnx @myininaya U are great. Nice help

29. koli123able

thanks

30. koli123able

got 2 values 9 and 5 of a

31. myininaya

Great! You go guys! :)

32. 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.

33. myininaya

The discriminant is $B^2-4AC$

34. Miyuru

How did it came.

35. Miyuru

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

36. 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.

37. Miyuru

So to slove the equation should i find a b c

38. Miyuru

*solve