any quick way to solve this?
For each of the following equations, find the value(s) of the constantαso that the equation has exactly one solution, and determine the solution for each value.

ax^2+x+1

Question

any quick way to solve this?
For each of the following equations, find the value(s) of the constantαso that the equation has exactly one solution, and determine the solution for each value.

ax^2+x+1

darkknight · Answer

that is supposed to be of the constant a so that the...

mhchen · Answer

|dw:1575227922315:dw|

something like this I suppose.

justjm · Answer

You'll need to use the quadratic discriminant

$b^2 - 4ac$

If the discriminant is greater than 0, you have two solutions. If the discriminant is 0, you have 1 solution. Less than 0 means no solutions.

So you are given the quadratic and they are asking for constant such that there is only 1 root. Thus, you must find the discriminant and set it to 0, then solve for a.

$ax^2+x+1$

$1^1 - 4(a)(1)=0$
$1 - 4a = 0$
a=1/4

justjm · Answer

Sorry, for less than 0 I meant no *real* solutions as there are still imaginary. But they won't show up on real cartesian coordinates.

darkknight · Answer

ok thanks