Quadratic function (unitary quadratic equation) discriminant calculator

The unary quadratic equation \(ax²+bx+c=0\) is a special case when the function value of the quadratic function \(y=ax²+bx+c\) is equal to zero. Some quadratic function problems can be solved by the relationship between the roots of the quadratic equations and the coefficients (that is, the Vedas theorem); the distribution of the roots of the quadratic equations can be directly determined by the quadratic function image; the image of the quadratic function The intersection with the x-axis and the position of the image can also be judged by discriminant.

(4ac-b²)/4a is not the formula for judging the y-axis, which is the ordinate of the vertices in the general formula;

The discriminant is derived from this:

\(y=ax²+bx+c\)

The formula is vertices as \(y=a(x+b/2a))²+(4ac-b²)/4a\)

Let's solve y=0

y=0 is: a(x+b/2a)²+(4ac-b²)/4a=0

Denominator: 4a²(x+b/2a)²+(4ac-b²)=0

4a²(x+b/2a)²=b²-4ac

The left side of the equation is a non-negative number, obviously:

When b²-4ac<0, there is no solution;

When b²-4ac=0, there is a solution;

When b²-4ac>0, there are two solutions;

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