Discriminant Calculator

A discriminant is a function of a polynomial equations of coefficients that expresses the nature of a quadratic equation's roots. The equations may distinguish between several sorts of responses, such as:

• We find two true solutions when the discriminant value is positive.
• There is just one actual solution when the discriminant value is zero.
• We get a pair of complex solutions when the discriminant value is negative.

The standard discriminant of an equation of the form ax²+bx+c = 0 is calculated using he below given formula:

Discriminant, D = b² – 4ac

Where

• D is the value of the discriminant
• a is the coefficient of x²
• b is the coefficient of x
• c is a constant term.

Let's go with the solved example on Discriminant Calculator and understand the concept practically in a step-wise manner.

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Examples on Finding Discriminant of Quadratic Equation

1. What should be the value of discriminant (D) in the equation 2x² - x + 4 ?

Solution:

Given that the quadratic equation is 2x² - x + 4

Here, a = 2, b = -1, c = 4

The discriminant formula is D = b² - 4ac

D = (-1)²- 4(2)(4)

D = 1 - 32

D = - 31

Thus, the discriminant is -31 of the equation 2x² - x + 4

2. What should be the value of discriminant (D) in the equation x² - 3x + 2 ?

Solution:

Given that the quadratic equation is x² - 3x + 2

Here, a = 1, b = -3, c = 2

The discriminant formula is D = b² - 4ac

D = (-3)²- 4(1)(2)

D = 9 - 8

D = 1

Therefore, the discriminant is 1 of the equation x² - 3x + 2

FAQs on Discriminant Calculator

1. Define discriminant?

A discriminant is a function of a polynomial equations of coefficients that expresses the nature of a quadratic equation's roots. The equations may distinguish between several sorts of responses, such as:

• We find two true solutions when the discriminant value is positive.
• There is just one actual solution when the discriminant value is zero.
• We get a pair of complex solutions when the discriminant value is negative.

2. Why is discriminant value important in a quadratic equation ?

The nature of the roots of the quadratic equation is revealed by discriminant value. Real or complex roots can be found in quadratic equations. It helps in the determination of an equation's solution.

3. What about the standard form of discriminant ?

The standard discriminant form for the quadratic equation ax² + bx + c = 0 is

Discriminant, D = b² – 4ac

Where

a be the coefficient of x²

b be the coefficient of x

c be a constant term.

4. How can the discriminant value be used to determine the nature of roots?

Different forms of roots can exist in a quadratic equation. The nature of roots is defined by the discriminant value. They are as follows:

• If D> 0, the roots are real and unequal
• If D = 0, the roots are real and equal
• If D < 0, the roots are not real (i.e., complex).

5. In a quadratic equation, why is discriminant value important ?

The nature of the roots of the quadratic equation is revealed by discriminant value. Real or complex roots can be found in quadratic equations. It aids in the determination of an equation's solution.