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The necessary and sufficient condition is
the discriminant of the quadratic equation is zero: d = b^2 - 4ac = 0,
referring to the standard form of the quadratic equation ax^2 + bx + c = 0.
In your case b= 2, c= 4, therefore the discriminant d = = 4 - 16a.
The condition d= 0 gives you an equation 4 - 16a = 0, or 16a = 4,
which implies a = = 0.25.
It is your
Answer. a = = 0.25.
Solved.
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To get introductory knowledge on quadratic equations, see the lessons
- Introduction into Quadratic Equations
- PROOF of quadratic formula by completing the square
in this site.