# Find Number Of Real Solutions Using Discriminant Worksheet

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The discriminant is essential in quadratic equations for determining the nature of the roots. For the quadratic equation $$ax^2 + bx + c = 0$$, the discriminant is calculated as $$b^2 - 4ac$$.

The value of the discriminant indicates:

If $$D > 0$$: Two distinct real roots.

If $$D = 0$$: One real root (repeated).

If $$D < 0$$: No real roots.

Algebra 2

## How Will This Worksheet on “Find Number of Real Solutions Using Discriminant” Benefit Your Student's Learning?

• It deepens our understanding of the nature of solutions for quadratic equations.
• It enhances our ability to analyze and evaluate mathematical problems, promoting logical and critical thinking skills.
• It improves problem-solving abilities by helping us determine the number and type of solutions available.

## How to Find Number of Real Solutions Using Discriminant?

• Identify the values of $$a$$, $$b$$, and $$c$$ from the given quadratic equation.
• Plug the values of $$a$$, $$b$$, and $$c$$ into the discriminant formula.
• Compute the value of $$D$$.
• Examine the discriminant to determine the nature of the roots.

## Solved Example

Q. Determine the number of real solutions for the quadratic equation $2x^2 - 3x + 1 = 0$ using the discriminant.
Solution:
1. Identify values: Identify the values of $a$, $b$, and $c$.$\newline$Compare $ax^2 + bx + c = 0$ and $2x^2 - 3x + 1 = 0$.$\newline$$a = 2$$\newline$$b = -3$$\newline$$c = 1$
2. Compare equations: Substitute $a = 2$, $b = -3$, and $c = 1$ into the discriminant formula $D = b^2 - 4ac$.$\newline$$D = (-3)^2 - 4 \cdot 2 \cdot 1$
3. Substitute into formula: Simplify the discriminant.$\newline$$D = 9 - 8$
4. Simplify discriminant: Calculate the final value of the discriminant.$\newline$$D = 1$
5. Calculate final value: Determine the number of real solutions based on the discriminant.$\newline$Since $D > 0$, there are $2$ real solutions.

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