It will then have 2 different roots
If the discriminant is zero than it will have have 2 equal roots
That its roots (solutions) are coincident.
C
what math flowchart can make it true
Given the quadratic equation ax^2 + bx + c =0, where a, b, and c are real numbers: (The discriminant is equal to b^2 - 4ac) If b^2 - 4ac < 0, there are two conjugate imaginary roots. If b^2 - 4ac = 0, there is one real root (called double root) If b^2 - 4ac > 0, there are two different real roots. In the special case when the equation has integral coefficients (means that all coefficients are integers), and b^2 - 4ac is the square of an integer, the equation has rational roots. That is , if b^2 - 4ac is the square of an integer, then ax^2 + bx + c has factors with integral coefficients. * * * * * Strictly speaking, the last part of the last sentence is not true. For example, consider the equation 4x2 + 8x + 3 = 0 the discriminant is 16, which is a perfect square and the equation can be written as (2x+1)*(2x+3) = 0 To that extent the above is correct. However, the equation can also be written, in factorised form, as (x+1/2)*(x+3/2) = 0 Not all integral coefficients.
true.
If the discriminant of a quadratic equation is positive, it indicates that the equation has two distinct real roots. This means that the graph of the equation intersects the x-axis at two points. A positive discriminant also suggests that the solutions are not repeated and that the parabola opens either upward or downward, depending on the leading coefficient.
It has one real solution.
If the discriminant of a quadratic equation is less than zero, it indicates that the equation has no real solutions. Instead, it has two complex (or imaginary) solutions that are conjugates of each other. This means the parabola represented by the quadratic equation does not intersect the x-axis.
a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.
It discriminates between the conditions in which a quadratic equation has 0, 1 or 2 real roots.
The discriminant must be a perfect square or a square of a rational number.
That the discriminant of the quadratic equation must be greater or equal to zero for it to have solutions. If the discriminant is less than zero then the quadratic equation will have no solutions.
In that case, the discriminant is not a perfect square.
If the discriminant of a quadratic equation is zero, it indicates that the equation has exactly one real solution, also known as a double root. This means the parabola represented by the quadratic touches the x-axis at a single point rather than crossing it. In other words, the vertex of the parabola lies on the x-axis.
There are two complex solutions.
That its roots (solutions) are coincident.
That its roots (solutions) are coincident.