Find the discriminant of the quadratic equation calculator

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Method and examples

Method

1. Discriminant and nature of roots of quadratic equation

Equation =

Find

`25x^2-30x+9=0`
`2x^2+5x-10=0`
`x^2+10x-56=0`
`4x^2+11x+10=0`
`x^2-2x=8`
`x^2-25=0`
`x^2+5x+3=0`
`9x^2-24x+16=0`

Table of Contents Show

What you will learn in this mini lesson
What you need to know about the Discriminant of a Quadratic Equation
What is the Discriminant in Math?
Example: Find the Discriminant of a Quadratic Equation
How do u find the discriminant of a quadratic equation?
How do you find the discriminant on a calculator?
How do you find the discriminant step by step?
What is the value of the discriminant for the quadratic equation 3 =

2. Find the quadratic equation whose roots are alpha and beta
Alpha (α) =
Beta (β) =

`3,-4` `-1/2,+2/3` `2,-2/3` `3sqrt(7),-3sqrt(7)` `sqrt(7),-sqrt(7)` `1+3sqrt(2),1-3sqrt(2)` `(3+5sqrt(3))/2,(3-5sqrt(3))/2` `(-3+5sqrt(3))/2,(-3-5sqrt(3))/2` `(-3+sqrt(3))/2,(-3-sqrt(3))/2`

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What you will learn in this mini lesson

You will learn how to find the Discriminant of a Quadratic Equations in Standard Form and its significance in solving Quadratic Equations. Our Step by Step Calculator allows you to compute the Discriminant of your own quadratic equation.

Quick Example
2x2 -12x+16 has the discriminant:
= b2 – 4*a*c
= (-12)2 – 4*2*16
= 144 – 128 = 16
Since 16>0 2x2 -12x+16 has two real solutions. That’s all 😉

What you need to know about the Discriminant of a Quadratic Equation

The Discriminant is the red part of the famous Quadratic Equation Formula below:

What is the Discriminant in Math?

The Discriminant D= b2-4*a*c is the part of the above Quadratic Equation. It is the part inside the square root.
The Discriminant ‘discriminates’ or ‘distinguishes’ 3 different types of solutions to the Quadratic Equation.

1) If the Discriminant D is greater than 0 then we can take the square root and we will have 2 real solutions.
2) If the Discriminant D is equal to 0 then we can take the square root of 0 and we will have 1 real solutions.
3) If the Discriminant D is less than 0 then we can take the square root of a negative number and we will have 2 complex solutions.

In below’s example we have a Discriminant D=49. Since it is a positive number we know that our Quadratic Equation 2x2+5x-3=0 has 2 real (non-complex) solutions.

What you take from this is that a Discriminant tells you the type of solution of any Quadratic Equation WITHOUT given you the actual solutions. Those solutions can be found using our handy Quadratic Equation Solver at: https://mikescalculators.com/solve-quadratic-equation/

Example: Find the Discriminant of a Quadratic Equation

What is the Discriminant of 2x2+5x-3?
The coefficients are a=2, b=5 and c=-3.
We plug those into the formula for Discriminant D= b2-4*a*c
to get D=52-4*2*(-3)
which simplifies to
25 – 8*(-3) = 25 + 24 = 49
implying the Discriminant is D=49.

Using the above Discriminant Calculator to solve 2x2+5x-3=0 we must enter the coefficients a=2, b=5 and c=-3.
With steps we see the Discriminant is D=49 .

Get it now? Try the above Discriminant Calculator a few more times or watch the video below.

How do u find the discriminant of a quadratic equation?

The discriminant is the formula b squared minus 4ac remembering that a, b and c are the coefficients of your quadratic in standard form. It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions.

How do you find the discriminant on a calculator?

The procedure to use the discriminant calculator is as follows:.

Step 1: Enter the coefficient values such as “a”, “b” and “c” in the given input fields..

Step 2: Now click the button “Solve” to get the output..

Step 3: The discriminant value will be displayed in the output field..

Discriminant, D = b2 – 4ac..

How do you find the discriminant step by step?

Quadratic Formula - Discriminant.

Step 1: calculate the discriminant, using the formula: Δ=b2−4ac..

Step 2: solve the quadratic equation, which depends on the sign of the discriminant Δ, which leads to three possible cases: Case 1 if Δ>0: then the quadratic equation has two solutions: x=−b−√Δ2aandx=−b+√Δ2a..

What is the value of the discriminant for the quadratic equation 3 =

What is the value of the discriminant for the quadratic equation -3 = -x² + 2x? Summary: The value of the discriminant for the quadratic equation -3 = -x² + 2x is 16.