Solve quadratic equations ax²+bx+c=0 with step-by-step solutions and graphical visualization
The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0, where a ≠0.
When discriminant > 0
The parabola crosses the x-axis at two points
When discriminant = 0
The parabola touches the x-axis at exactly one point
When discriminant < 0
The parabola doesn't intersect the x-axis
The discriminant (b² - 4ac) determines the nature of the roots. If positive, there are two real roots; if zero, one repeated root; if negative, two complex roots.
No, if a = 0, the equation becomes linear (bx + c = 0) rather than quadratic. The coefficient 'a' must be non-zero for a quadratic equation.
Complex roots come in conjugate pairs (a + bi and a - bi). They indicate that the parabola doesn't cross the x-axis, meaning no real solutions exist for the equation.