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

Question 1143372: One root of is -4. Find the value of k.
Here is what I tried at the start:

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)   (Show Source): You can put this solution on YOUR website!
One root of is -4. Find the value of k.
:
continuing what you have

b becomes +3

multiply both sides by 2

subtract 3 from both sides

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)   (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)   (Show Source): You can put this solution on YOUR website!
One root of is -4. Find the value of k.
Here is what I tried at the start:

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(52858)   (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

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