# Find The Discriminant Of Quadratic Equations Worksheet

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The discriminant is a key concept in quadratic equations used to determine the nature of the roots. Represented by the symbol $$\Delta$$ (the uppercase Greek letter Delta), it is calculated using the coefficients of the quadratic function. The discriminant provides insight into the type of solutions a quadratic equation has. The formula for the discriminant is:

$$\Delta = b^2 - 4ac$$

, or

$$D = b^2 - 4ac$$

In these worksheets, students will calculate the value of the discriminant using this formula.

Algebra 2
Quadratic Equations

## How Will This Worksheet on “Find the Discriminant of Quadratic Equations” Benefit Your Student's Learning?

• It aids in understanding the nature of the roots—whether they are two real, one real, or imaginary.
• It enhances problem-solving skills by helping us determine the number of solutions and their types.
• Additionally, it allows us to decompose the quadratic equation into simpler components, facilitating the resolution of more complex problems.

## How to Find the Discriminant of Quadratic Equations?

• Determine the values of $$a$$, $$b$$, and $$c$$ from the given quadratic equation.
• Insert the values of $$a$$, $$b$$, and $$c$$ into the discriminant formula.
• Compute the value of $$D$$.

## Solved Example

Q. Find the discriminant. $\newline$$2q^2 - 9q + 8 = 0$$\newline$______
Solution:
1. Identify coefficients: Identify the coefficients of the quadratic equation.$\newline$The quadratic equation is in the form $ax^2 + bx + c = 0$. For the equation $2q^2 - 9q + 8 = 0$, the coefficients are:$\newline$$a = 2$$\newline$$b = -9$$\newline$$c = 8$
2. Calculate discriminant: Calculate the discriminant using the formula $D = b^2 - 4ac$.$\newline$Substitute the identified values into the formula:$\newline$$D = (-9)^2 - 4 \times 2 \times 8$
3. Perform calculations: Perform the calculations to find the value of the discriminant.$\newline$$D = 81 - 4 \times 2 \times 8$$\newline$$D = 81 - 64$$\newline$$D = 17$

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