SOLUTION: i'm trying to help my daughter with homework over the phone she is trying to solve the equation x^2 + bx + c = 0 when x = -4 or 6, what are b and c haven't a clue where to start

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Question 392768: i'm trying to help my daughter with homework over the phone
she is trying to solve the equation x^2 + bx + c = 0
when x = -4 or 6, what are b and c
haven't a clue where to start
Found 4 solutions by Alan3354, stanbon, ewatrrr, solver91311:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
x^2 + bx + c = 0
when x = -4 or 6, what are b and c
-------------------
x = -4 or 6 --> (x + 4)*(x - 6) = 0
-->
b = -2
c = -24
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
solve the equation x^2 + bx + c = 0
when x = -4 or 6, what are b and c
-----
If x = -4 you get: (-4)^2+b(-4)+c = 0
16-4b+c = 0
-4b+c = -16
-------------
If x = 6, you get: (6)^2+b(6)+c = 0
6b+c = -36
-----------
Now you have 2 equations with variables b and c.
-4b+c = -16
6b+c = -36
------------
Subtract the top equation from the lower one and solve for "b":
10b = -20
b = -2
-----
Solve for c by substituting into 6b+c = -36:
6*-2+c = -36
-12+c = -36
c = -24
------------------
Check in the equation -4b+c = -16
-4*-2+(-24) = -16
8-24 = -16
-16 = -16
============================
Cheers,
Stan H.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

Given x = -4 or 6, those are the 'roots' of the quadratic equation and 

Note: 

  y = (x - (-4))(x-6)

  y = (x+4)(x-6)     |multiplying gives us

  y = x^2 + 4x - 6x - 24

  y = x^2 - 2x - 24 = 0

therefore, in this example of a standard quadratic equation y = x^2 + bx + c

 b = -2 and c = -24



  

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
 





If











and











(which must be true since you were given two different real number roots for the original equation)





Then there are two numbers  and  such that











You are given  and  so:











Just multiply (using FOIL):











and the resulting coefficients on the 1st degree and constant terms will be your values for  and .





John



My calculator said it, I believe it, that settles it


The Out Campaign: Scarlet Letter of Atheism


 

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