# If the discriminant of a quadratic equation is zero the equation will have_____________ roots. Does anyone know the answer.

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### 1 Answer

A quadratic equation can be written in the form `y=ax^2+bx+c` .

(`a!=0` )

The discriminant is defined to be `D=b^2-4ac` .

Now, consider the "quadratic equation": the solution to a quadratic is given by `x=(-b+-sqrt(b^2-4ac))/(2a)` . The axis of symmetry is the line `x=-b/(2a)` and the solutions (zeros) are symmetric about the axis of symmetry. Note also that you are taking the square root of the discriminant.

If `b^2-4ac<0` then there are no real roots, as you cannot take the square root of a negative number in the reals.

If `b^2-4ac>0` then there are 2 real roots (zeros, solutions) since they are symmetric about the axis of symmetry.

If `b^2-4ac=0` then you move 0 units to the left and right of the axis of symmetry -- in other words the only root is on the axis of symmetry. This point is the vertex of the parabola.

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**If the discriminant of a quadratic equation is zero, then there is exactly 1 real root (zero,solution) to the quadratic.**

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** The root found is called a repeated root, or a root of multiplicity 1.**

Example: `y=(x+1)^2=x^2+2x+1` . The discriminant is `2^2-4(1)(1)=0` . Clearly the only solution is x=-1.

The graph: