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For what value of b does 4x^2 - bx + 12 = 0 have only one root.

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xetaalpha | Student | (Level 2) Honors

Posted June 21, 2013 at 4:28 PM via web

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For what value of b does 4x^2 - bx + 12 = 0 have only one root.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 21, 2013 at 4:32 PM (Answer #1)

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The roots of a quadratic equation ax^2 + bx + c = 0 are `(-b+-sqrt(b^2-4ac))/(2a)` .

If b^2 - 4ac = 0, the equation has equal roots.

For 4x^2 - bx + 12 = 0 to have equal roots, b^2 = 4*4*12

=> b^2 = 192

=> `b = +-8*sqrt 3`

The required value of `b = +- 8*sqrt 3`

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