Firejay5 2 years ago Solve and show and explain work x^2 + bx + c = 0

1. LogicalApple

Try applying the quadratic equation to this one.

2. Firejay5

@LogicalApple

3. LogicalApple

$x = \frac{ -b \pm \sqrt{b^{2} - 4ac} }{ 2a }$

4. Firejay5

@BubbaMurphy Do you have a different way to do this problem???

5. BubbaMurphy

LogicApple's way is definitely the way to do it.

6. BubbaMurphy

in this case, a=1

7. Firejay5

Is that really how yo would solve it

8. Firejay5

would A, B, and C = 1

9. LogicalApple

Based on the equation you supplied, a = 1, b = b, and c = c.

10. LogicalApple

They are coefficients of whatever quadratic you are talking about. Did you have a quadratic in mind?

11. Firejay5

what you mean

12. LogicalApple

$6x^{2} - 9x + 12 = 0$ $-5x^{2} + x - 10 = 0$ $x^2 + x - 1 = 0$ These are some examples of quadratics, all set equal to 0.

13. Firejay5

Yea I know that

14. LogicalApple

Oh, ok... so what is your question?

15. Firejay5

We have to solve x^2 + bx + c = 0 for bonus and I have no idea what to do

16. LogicalApple

I suggested using the quadratic equation. The only difference between x^2 + bx + c = 0 and the quadratics that I mentioned is that the coefficients in your equation are only known by their variable letter. But that is ok, you can still apply the quadratic formula to them. The solutions to x^2 + bx + c = 0 is: $\frac{ -b \pm \sqrt{b^{2} - 4c} }{ 2 }$ This is the same thing I wrote before, except I let a = 1 because the coefficient of x^2 in your equation is 1.

17. Firejay5

We didn't learn that equation you gave me

18. LogicalApple

What about completing the square ?

19. Firejay5

20. LogicalApple

Yes, but you would arrive at the same answer if you complete the square. Both techniques are valid for solving quadratic equations.

21. Firejay5

I have to show my work, so how would I show it

22. LogicalApple

Well if you're using the quadratic equation you could say "applying the quadratic equation". But if you wanted to complete the square then: |dw:1359081924838:dw|

23. Azteck

I think you can use sum and product of roots: $\alpha +\beta= \frac{ -b }{ a }$ $\alpha \beta=\frac{ c }{ a }$

24. Firejay5

b^2/4

25. LogicalApple

26. LogicalApple

|dw:1359082578453:dw|

27. LogicalApple

(b/2)^2 = b^2/4

28. Firejay5

After (x + b/2)^2 = b^2/4 - c. Find the square root of both.

29. LogicalApple

Yes

30. Firejay5

I got x + b/2 = b/4 - c. Is that correct?

31. LogicalApple

no the square root of both sides gives: x + b/2 = ± sqrt(b^2/4 - c)

32. Firejay5

what then

33. LogicalApple

All the steps are in the picture attached.

34. Firejay5

I am sorry the last step in attachment is the answer

35. LogicalApple

Oh ok did you get it figured out ?

36. Firejay5

so x = +/- sqrt b^2 - 4c /2 is the answer

37. LogicalApple

|dw:1359083804186:dw| yes

38. Firejay5

Will you forgive me @LogicalApple ?

39. LogicalApple

What for? It's a learning experience

40. Firejay5

I probably annoyed you a lot