Question 1159785
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The line  y = 2x+c is a tangent to the curve y = 2x^2-6x+20. Find the value of c.
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            Notice that I EDITED your post, since it was nonsensical in your original version.



<pre>
Actually, it is of the pure Algebra problem, and can be solved using Algebra methods,

without disturbing Calculus.


You simply need to find the unique common points of the straight line and the parabola.

Watch my steps.


I will search for a unique common point of the straight line and the parabola.

So, I write this equation

    2x + c  = 2x^2 - 6x + 20    (1)


and simplify it 

    2x^2 - 8x + (20-c) = 0.     (2)


Next I calculate the discriminant

    d = {{{b^2 - 4*a*c)}}} = (-8)^2 - 4*2*(20-c) = 64 - 160 + 8c = 8c - 96.


Since I want to have a unique root of the quadratic equation (1)  ( or (2) ), I equate the discriminant to 0 (zero)

    8c - 96 = 0,


and I get the solution immediately

    c = 96/8 = 12.     <U>ANSWER</U>
</pre>

Solved.