A quadratic expression when equated to zero is called a quadratic equation. A quadratic equation looks like this ax
^{2} + bx + c = 0.x = (-b ± √(b ^{2} - 4ac))/2aAs we can see there are two values which satisfy the equation hence the number of solutions is two and there are two roots. As the solutions of a quadratic equation are called roots. Let us analyze the roots i.e. when they are real. The value under the square root is positive if b ^{2} - 4ac is positive. When such condition arises then the roots are real. The value b^{2} - 4ac is called the discriminant. If the discriminant is equal to zero then both the roots are equal. If the discriminant is negative then both the roots are imaginary and they occur in conjugate pairs. If the roots are real and distinct then the graph cuts the x-axis at two different points. If the roots are real and equal then the graph cuts the x-axis at one point. If the roots are imaginary then the graph does not cut the x-axis.The graph below shows two real roots. x ^{2} + 5x - 2 = 0The graph below shows two real roots x ^{2} + 5x + 6.25 = 0The graph below represents when roots are imaginary. |

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