It is simply an equation with non-rational solutions. There is no special name for it.
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Quadratics can two, one or no real roots.
If the discriminant of a quadratic equation is 0 then it has two equal real roots.
That depends on the value of its discriminant if its less than zero then it has no 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.
The equation ax^2 + bx + c = 0 where a, b and c are real and a is non-zero has discriminant D = b^2 – 4ac. Then,if D > 0 the equation has two real roots which are distinct;if D = 0 the equation has two real roots which are coincident;if D < 0 the equation has two roots which form a complex conjugate pair (advanced mathematics only).