![]() Note*: Solution to such quadratic equations can be complex but it is beyond the scope of books that we study in tenth grade. Or, you can say there is no real solution for this quadratic equation. Therefore, there will be no solution for this quadratic equation. We all know that square of negative number does not exist. ![]() You can also verify this by actually trying to find the roots of equation. Therefore, discriminant of equation is less than zero. You can also verify this by actually finding the roots of equation. Therefore, equation has equal and real roots. Therefore, discriminant of equation is equal to zero. You can also verify this by actually finding roots of equation. ![]() Therefore, equation has real and distinct roots. Therefore, discriminant of equation is greater than 0. We will now determine nature of roots of these three quadratic equations using discriminant.Ĭomparing this equation with general form Suppose, we have three quadratic equations: Lets take three different examples, one for each case. If, Discriminant < 0, then there are no real roots for given quadratic equation. If, Discriminant =0, then two roots of quadratic equation are real and equal. If, Discriminant >0, then two roots of quadratic equation are distinct and real. ![]() Now, the question is how can we determine nature of roots from the value of discriminant of quadratic equation. Similarly, we can find discriminant of other quadratic equations. , if we compare it with general form of quadratic equation Lets take an example, we have quadratic equation, Therefore, discriminant of any quadratic equation = ) of quadratic formula is called discriminant of quadratic equation. To find roots of any given quadratic equation.
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