What happens if the discriminant is zero

What is a discriminant in algebra? Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. What can the discriminant tell you? The discriminant tells us the following information about a quadratic equation: If the solution is a real number or an imaginary number. If the solution is rational or if it is irrational. If the solution is one unique number or two different numbers.

How many solutions would a quadratic equation have if the discriminant is 12? If the discriminant of a quadratic equation is 12 , then it has two distinct real roots. Note that 12 is not a perfect square, so if the coefficients of the quadratic are integers or otherwise rational, then the roots are both irrational.

How tight should fittings be water cooling? What happens if you dont bench bleed a master cylinder? This is false. Then state how many roots it has, and whether they are real or imaginary. Finally, use the quadratic function to find the exact roots of the equation. One real root:. Two real roots: or. Two imaginary roots:. When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root.

When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.

In this case, we have two real roots. Exact Roots:. In this case, we have two distinct imaginary roots. In other words, our two distinct imaginary roots are and. Two distinct real roots:. Two distinct imaginary roots:. In this case, there is exactly one real root. Because , this simplifies to. We can further simplify this to. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. If the discriminant of a quadratic function is greater than zero, that function has two real roots x -intercepts. Taking the square root of a positive real number is well defined, and the two roots are given by,.

This function is graphically represented by a parabola that opens upward whose vertex lies below the x -axis. Thus, the graph must intersect the x -axis in two places i.

In the next section we will use the quadratic formula to solve quadratic equations. We can do this by completing the square as, Solving for x and simplifying we have, Thus, the roots of a quadratic function are given by, This formula is called the quadratic formula , and its derivation is included so that you can see where it comes from. Specifically, if 1. One to one online tuition can be a great way to brush up on your Maths knowledge. Answered by Alistair G. Answered by Oliver P. Answered by Evelyn H.

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