Question

A quadratic equation has exactly one real number solution. Which is the value of its discriminant?


−1

0

1

2

Answer 1

The discriminant, is an essential component of the quadratic formula:
\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
The discriminant allows us to predict wether or not a quadratic function posseses any zeroes or "roots", this implying \(ax^2 \pm bx \pm c=0\).
Now, we can define the discriminant as the "set of operations inside the radical" of the quadratic formula, this being notated with the greek letter capital Delta:
\[\Delta = b^2-4ac\]
Now, since the discriminant is the number that will be inside the radical (the square root), there will be some restrictions and these restrictions impact the result for "x".

Answer 2

@Owlcoffee has a good explanation but I would stick with \[\Large ax^2 + bx + c = 0\] instead of \[\Large ax^2 \pm bx \pm c = 0\]

the first one would allow a,b,c to be positive or negative. The second one is a bit ambiguous in my opinion and it could lead to multiple branches

Answer 3

this page offers a good explanation I think

http://www.regentsprep.org/regents/math/algtrig/ate3/discriminant.htm