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

1. koli123able Group Title

how should i start

2. myininaya Group Title

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

3. koli123able Group Title

D=b^2-4ac

4. myininaya Group Title

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 Group Title

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

6. myininaya Group Title

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

7. myininaya Group Title

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

8. myininaya Group Title

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

9. koli123able Group Title

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

10. koli123able Group Title

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

11. myininaya Group Title

Yep! :)

12. myininaya Group Title

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

13. myininaya Group Title

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

14. koli123able Group Title

ok wait

15. koli123able Group Title

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

16. myininaya Group Title

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

17. koli123able Group Title

yeah -28a

18. koli123able Group Title

a^2-14a+53=0

19. koli123able Group Title

is it right

20. myininaya Group Title

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

21. myininaya Group Title

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

22. koli123able Group Title

a^2-14a+45=0

23. myininaya Group Title

yep do you know how to factor?

24. koli123able Group Title

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

25. myininaya Group Title

The quadratic formula? That is fine. :)

26. koli123able Group Title

yes

27. Miyuru Group Title

I solved it by factors..

28. Miyuru Group Title

thnx @myininaya U are great. Nice help

29. koli123able Group Title

thanks

30. koli123able Group Title

got 2 values 9 and 5 of a

31. myininaya Group Title

Great! You go guys! :)

32. myininaya Group Title

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 Group Title

The discriminant is $B^2-4AC$

34. Miyuru Group Title

How did it came.

35. Miyuru Group Title

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

36. myininaya Group Title

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \text{ is called the quadratic formual }$ 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 Group Title

So to slove the equation should i find a b c

38. Miyuru Group Title

*solve