To find the discriminant of a quadratic equation, you need to identify the equation in the standard form:

$ax^2 + bx + c = 0$

The discriminant $\Delta$ is given by the formula:

$\Delta = b^2 - 4ac$

Where:

• $a$ is the coefficient of $x^2$,
• $b$ is the coefficient of $x$,
• $c$ is the constant term.

The discriminant helps to determine the nature of the roots:

• If $\Delta > 0$, the equation has two distinct real roots.
• If $\Delta = 0$, the equation has one real root (a repeated root).
• If $\Delta < 0$, the equation has two complex roots.

Example:

For the quadratic equation $2x^2 - 4x + 3 = 0$, the coefficients are:

• $a = 2$,
• $b = -4$,
• $c = 3$.

Using the formula for the discriminant:

$\Delta = (-4)^2 - 4(2)(3) = 16 - 24 = -8$

Thus, $\Delta = -8$, so the equation has two complex roots.

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Do you have a specific quadratic equation you would like me to help with? Feel free to upload a photo of the equation if needed!

Relative Questions:

1. What does it mean if the discriminant is negative?
2. Can the discriminant be applied to other types of polynomials?
3. How does the discriminant relate to the graph of a quadratic function?
4. How can you factor a quadratic if the discriminant is a perfect square?
5. What is the geometric significance of the discriminant?

Tip: The discriminant helps you decide whether a quadratic equation is factorable or not without solving it entirely.