SOLUTION: One root of {{{ x^2-3x+k-2=0 }}} is -4. Find the value of k. Here is what I tried at the start: {{{ -4=-3+- sqrt(9-4(k-2))/2 }}} But I am stuck from there on. Thank you for

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: One root of {{{ x^2-3x+k-2=0 }}} is -4. Find the value of k. Here is what I tried at the start: {{{ -4=-3+- sqrt(9-4(k-2))/2 }}} But I am stuck from there on. Thank you for       Log On


   

Question 1143372: One root of +x%5E2-3x%2Bk-2=0+ is -4. Find the value of k.
Here is what I tried at the start:
+-4=-3%2B-+sqrt%289-4%28k-2%29%29%2F2+
But I am stuck from there on. Thank you for your help!
Found 4 solutions by ankor@dixie-net.com, rothauserc, MathTherapy, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One root of +x%5E2-3x%2Bk-2=0+ is -4. Find the value of k.
:
continuing what you have
+%28-%28-3%29-sqrt%289-4%28k-2%29%29%2F2%29+=+-4
b becomes +3
+%283-sqrt%289-4%28k-2%29%29%2F2%29+=+-4
multiply both sides by 2
+%283-sqrt%289-4%28k-2%29%29%29+=+-8
subtract 3 from both sides
+%28-sqrt%289-4%28k-2%29%29%29+=+-11
square both sides
9 - 4(k-2) = 121
-4k + 8 = 121 - 9
-4k = 112 - 8
-4k = 104
k = 104/-4
k = -26
:
:
check: the equation then is: y = x^- 3x - 28
factors to (x+4)(x-7)

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Since one root is -4, then x+4 must divide the polynomial
:
(x^2 -3x +k -2)/(x+4) = x-7 with remainder k +26
:
we know the remainder must be 0, then
:
k +26 = 0
:
k = -26
:

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
One root of +x%5E2-3x%2Bk-2=0+ is -4. Find the value of k.
Here is what I tried at the start:
+-4=-3%2B-+sqrt%289-4%28k-2%29%29%2F2+
But I am stuck from there on. Thank you for your help!
You could use the quadratic equation formula, but I prefer the method below:

You may remember that: 

Let's call the other root: R2. We can see from the quadratic equation that: a = 1; b = - 3, and c = k - 2 

We then get: 

We also get: 

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AND an even easier method is the REMAINDER THEOREM method used by TUTOR @Rothauserc, which should actually be:

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.

The EASIEST way to solve it is to substitute x= -4 into the equation and use the fact that "-4" is the root:


4^2 - 3*(-4) + k - 2 = 0


16 + 12 + k - 2 = 0


k + 26 = 0


k = -26.      ANSWER