Question 390472: find the second root of the quadratic equation x^2 + 9x + k = 0 if one root is -2. Found 2 solutions by stanbon, richard1234:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! find the second root of the quadratic equation
x^2 + 9x + k = 0 if one root is -2.
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Using synthetic division you get:
-2)....1....9....k
.........1....7...|k-14
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Solve k-14 = 0
k = 14
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Notice the quotient is x+7
So the 2nd root is x=-7
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Cheers,
Stan H.
You can put this solution on YOUR website! A fast way to solve this problem is to know that the sum of the roots of a quadratic is , or -9 in this case. Since one of the roots is -2, the other one must be (-9) - (-2), or -7. Amazing that we don't even need to solve for k to find the other root?
(In general, the sum of the roots of any polynomial is -b/a. This is one of Vieta's formulas.
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