SOLUTION: b=a+c, than the equation ax2+bx+c=0 has a) real root b)no real root c) equal root d) no root

Question 1136663: b=a+c, than the equation ax2+bx+c=0 has
a) real root b)no real root c) equal root d) no root
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it appears tha this will give you real roots.
in fact, it appears that one of the roots will be plus or minus c/a and the other root will be -1.

here's my worksheet that derives what i think is the answer.

$$$

apparently one of the roots will be -c/a and the other root will be -1.

i tested this out with various value of b = c + a to see if that was true.

as far as i can tell, it is.

i chose to test this against a quadratic solver.

i chose the following scenarios.

a     b     c       root 1     root 2
-5    -25   -20     -4         -1
-5    +15   +20     -1         +4
+5    -15   -20     -1         +4
+5    +25   +20     -4         -1

in all of these scenarios, b = a + c.

one of the roots was -c/a and the other root was -1, as i had derived in the worksheet, confirming that the derivation was correct.

here's the results from the quadratic solver.

$$$

your solution is selection (a) real root
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