Question

for the following quadratic equation, find the discriminant.

\\5x^2 - 22x + 87 = -6x - 8\\

Explanation:

Write the equation in standard form

To find the discriminant, we first rewrite the given quadratic equation in standard form:

$$ax^2 + bx + c = 0$$

We start with the given equation:

$$5x^2 - 22x + 87 = -6x - 8$$

Add \(6x\) and \(8\) to both sides of the equation:

$$5x^2 - 22x + 6x + 87 + 8 = 0$$

$$5x^2 - 16x + 95 = 0$$

Identify the coefficients

From the standard form \(5x^2 - 16x + 95 = 0\), we identify the coefficients:

$$a = 5$$

$$b = -16$$

$$c = 95$$

Calculate the discriminant

The formula for the discriminant \(D\) of a quadratic equation is:

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

Substitute the identified coefficients into the formula:

$$D = (-16)^2 - 4(5)(95)$$

$$D = 256 - 1900$$

$$D = -1644$$

Answer:

\(-1644\)