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For the following quadratic equation, find the discriminant.

3x^(2)+18 x-81=4x^(2)
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $3 x^{2}+18 x-81=4 x^{2}$ $\newline$ Answer:

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Solve exponential equations by rewriting the base

Full solution

Q. For the following quadratic equation, find the discriminant.

\newline

3 x^{2}+18 x-81=4 x^{2}

\newline

Answer:

Rearrange into Standard Form: First, we need to rearrange the quadratic equation into standard form, which is $ax^2 + bx + c = 0$ . We have the equation $3x^2 + 18x - 81 = 4x^2$ . Let's move all terms to one side to get it into standard form. Subtract $4x^2$ from both sides to get $-x^2 + 18x - 81 = 0$ . Now, we multiply through by $-1$ to make the $x^2$ term positive, which gives us $x^2 - 18x + 81 = 0$ .
Identify Coefficients: Now that we have the quadratic equation in standard form, we can identify the coefficients $a$ , $b$ , and $c$ . From the equation $x^2 - 18x + 81 = 0$ , we have: $a = 1$ , $b = -18$ , and $c = 81$ .
Calculate Discriminant: The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . Let's calculate the discriminant using the identified coefficients. $D = (-18)^2 - 4(1)(81)$
Perform Calculations: Now, we perform the calculations. $\newline$ $D = 324 - 4(81)$ $\newline$ $D = 324 - 324$ $\newline$ $D = 0$

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