Why do quadratic equations only have two solutions?

There are usually two solutions because quadratic equations form a parabola in Cartesian coordinates. In almost any case involving a function, the parabola will intercept the x-axis at two points. Those two points are the two x values that cause the function to be equal to zero.

Do quadratic equations always have two distinct solutions?

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

How do you know if a quadratic equation has one two or no solution?

The discriminant is the expression b2 – 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

Do quadratic equations always have two roots?

Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.

How many solutions can a quadratic equation have and why does it vary?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

How do you know if a quadratic equation has one two or three roots?

To work out the number of roots a qudratic ax2​+bx+c=0 you need to compute the discriminant (b2​-4ac). If the discrimant is less than 0, then the quadratic has no real roots. If the discriminant is equal to zero then the quadratic has equal roosts. If the discriminant is more than zero then it has 2 distinct roots.

Why quadratic equations have two roots?

Except α and β no other values of x satisfies the equation ax2 + bx + c = 0. Hence, we can say that the equation ax2 + bx + c = 0 has two and only two roots. Therefore, a quadratic equation has two and only two roots.