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The discriminant of the zero polynomial, P(x) = 0, is zero because it has multiple roots at every point: For all x, P'(x) = P(x) = 0. Thus, the formula for the discriminant gives
Δ = a_0^(0-2) * Π_{all different roots counting multiplicity} (one root - other root)^2
Note that the second term contains an uncountable number of zeroes multiplied together. Dividing out two of them leaves you with an uncountable number of zeroes multiplied together-- i.e. zero.
The above argument can be made more rigorous by adding in all the limits and stuff.
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What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
If the discriminant of an equation is zero is true of the equation?
That its roots (solutions) are coincident.
If the discriminant equals zero the equation has solution?
one
What is true of an equation if its discriminant is zero?
it has one real solution
When can you say that the discriminant don't have root?
If the discriminant of a quadratic equation is less than zero then it will have no real roots
What can the discriminant tell you about a quadratic equation?
It can tell you three things about the quadratic equation:- 1. That the equation has 2 equal roots when the discriminant is equal to zero. 2. That the equation has 2 distinctive roots when the discriminant is greater than zero. £. That the equation has no real roots when the discriminant is less than zero.
If the discriminant of an equation is 0?
If the discriminant of a quadratic equation is zero then it has two identical roots.
If the discriminant of an equation is zero then?
The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
What are 3 outcomes for the discriminant?
If the discriminant of a quadratic equation is zero then it has equal roots. If the discriminant is greater than zero then there are two different roots. If the discriminant is less than zero then there are no real roots.
What is a discriminant in a quadratic equation?
General form of a quadratic equation is: ax2+b+c = 0 The discriminant is: b2-4ac If the discriminant equals zero then there are two equal roots If the discriminant is greater than zero then there are two different roots If the discriminant is less than zero then there are no real roots
If the discriminant of an equation is zero What is true of the equation?
That its roots (solutions) are coincident.
If the discriminant of an equation is zero is true of the equation?
That its roots (solutions) are coincident.
If the discriminant equals zero the equation has solution?
one
When will an equation have no solution?
If the discriminant of a quadratic equation is less than zero then it has no solutions.
If the discriminant is zero the equation has solutions?
It has 2 equal solutions
What is true of an equation if its discriminant is zero?
it has one real solution
