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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
