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Using the general equation for the roots of a quadratic equation what is the value of k...

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xetaalpha | Student | (Level 2) Honors

Posted March 10, 2013 at 6:11 AM via web

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Using the general equation for the roots of a quadratic equation what is the value of k if the equation x^2 + (3+k)x + 3*k = 0 has roots 4 and -1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 10, 2013 at 6:22 AM (Answer #1)

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If the roots of a quadratic equation are a and b, the quadratic equation is x^2 - (a+b)*x + a*b = 0

The roots of the equation x^2 + (3+k)*x + 3*k = 0 are 4 and -1. This gives -(3 + k) = 4 - 1 = 3 and 3*k = -1*4.

-(3 + k) = -3

=> -3 - k = -3

=> k = 0

But for this value of k, `3*k != -4` .

There is no value of k for which the equation x^2 + (3+k)*x + 3*k = 0 has roots 4 and -1.

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