Question 1143372
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 your help!
<pre>You could use the quadratic equation formula, but I prefer the method below:
You may remember that: {{{matrix(2,7, The, SUM, of, the, ROOTS, "=", - b/a, The, PRODUCT, of, the, ROOTS, "=", c/a)}}}
Let's call the other root: R<sub>2</sub>. We can see from the quadratic equation that: a = 1; b = - 3, and c = k - 2 
We then get: {{{matrix(1,11, - 4 + R[2], "=", - - 3/1, "=====>", R[2], "=", 3 + 4, "=====>", R[2], "=", 7)}}}
We also get: {{{highlight(highlight_green(highlight(matrix(1,13, R[1](R[2]), "=", (k - 2)/1, "=====>", - 4(7), "=", k - 2, "======>", - 28 + 2, "=", k, "=====>", highlight(matrix(1,3, - 26, "=", k))))))}}}
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AND an even easier method is the REMAINDER THEOREM method used by TUTOR @Rothauserc, which should actually be:
{{{highlight_green(matrix(5,3, f(x), "=", x^2 - 3x + k - 2, f(- 4), "=", (- 4)^2 - 3(- 4) + k - 2, 0, "=", 16 + 12 + k - 2, 0, "=", 26 + k, - 26, "=", k))}}}