# SOLUTION: one root of the quadratic equation x2-kx+8=0 is negative of the other. the value of k is

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 Click here to see ALL problems on Quadratic Equations Question 414332: one root of the quadratic equation x2-kx+8=0 is negative of the other. the value of k is Found 2 solutions by Edwin McCravy, Theo:Answer by Edwin McCravy(13211)   (Show Source): You can put this solution on YOUR website! one root of the quadratic equation x²-kx+8=0 is negative of the other. the value of k is -------------------------------------- ``` There are two ways to do this: First way: Let the roots be +r and -r Then x² - kx + 8 = 0 whould have to factor as (x - r)(x + r) = 0 which multiplies out to x² + rx - rx + r² = 0 x² + r² = 0 So since the terms in x cancel, the coefficient of r must be zero, which makes k = 0. However the roots are imaginary since r² must equal to 8 x² + 8 = 0 x² = -8 __ x = ±Ö-8 ___ x = ± iÖ4*2 _ x = ±2iÖ2 ------------------------ The other way to do it is to use the quadratic formula: x² - kx + 8 = 0 The two roots are and Setting one equal to the negative or the other: Multiply through by 2 Subtracting the radical from both sides: k = -k 2k = 0 k = 0 And the two roots are Edwin``` Answer by Theo(5548)   (Show Source): You can put this solution on YOUR website! your equation is x^2 - kx + 8 = 0 unless i completely misunderstand what you are asking for, there is no solution to this equation as far as i can see. if one root is the negative of the other root, then you can never get a positive constant value in the equation. the only way one root could be the negative of the other is if the roots were equal with opposite signs. if the roots were equal, then they would each have to be equal to square root of 8 because the square root of 8 times the square root of 8 equals 8. for one of the roots to be a negative of the other, then: one of the roots would have to be plus the square root of 8. the other root would have to be minus the square root of 8. plus the square root of 8 times minus the square root of 8 would result in minus 8. but you want them to be equal to plus 8. can't be done.