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How do you find the values of k when the straight line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?
Wiki User
∙ 13y ago
By implication : x2-8x+7 = kx-2
Form a quadratic equation: x2-8x-kx+9 = 0
For a line to be a tangent to the curve it must have two equal roots and the discriminant b2-4ac of the quadratic equation must equal 0.
So: (-8-k)2-4*1*9 = 0
(-8-k)2-36 = 0
(-8-k)2 = 36
Square root both sides:
-8-k = -/+6
-k = 2 or 14
k = -2 or -14
When k = -2 is substituted into the quadratic equation x will have two equal roots of 3
When k = -14 is substituted into the quadratic equation x will have two equal roots of -3
Wiki User
∙ 13y ago
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