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What is m if curve x^2-(m-3)x+m passes through x axis one time?

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rouche | Student, Undergraduate | (Level 1) Honors

Posted July 10, 2012 at 3:10 PM via web

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What is m if curve x^2-(m-3)x+m passes through x axis one time?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 10, 2012 at 3:30 PM (Answer #1)

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The problem provides the information that the graph touches x axes one time, hence, the quadratic equation has two equal roots.

You should remember the case a quadratic equation `ax^2 + bx + c = 0`  has two equal solutions such that:

`Delta = 0 =gt b^2 - 4ac = 0`

Comparing the given equation to standard form of quadratic yields `a = 1 , b = -(m-3) , c = m` .

Substituting these values in formula of `Delta`  yields:

`Delta = (3-m)^2 - 4m`

You should expand the square such that:

`9 - 6m + m^2 - 4m = 0`

`m^2 - 10m + 9 = 0`

You should use quadratic formula to find m such that:

`m_(1,2) = (10+-sqrt(100-36))/2`

`m_(1,2) = (10+-sqrt64)/2`

`m_(1,2) = (10+-8)/2`

`m_1 = 9 ; m_2 = 1`

Hence, evaluating the possible values for m that follows the given conditions yields `m_1 = 9`  and `m_2 = 1` .

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