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For the following quadratic equation, find the discriminant.

-7x^(2)+54 x-231=-4x^(2)
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-7 x^{2}+54 x-231=-4 x^{2}$ $\newline$ Answer:

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Transformations of functions

Full solution

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

\newline

-7 x^{2}+54 x-231=-4 x^{2}

\newline

Answer:

Bring to Standard Form: First, we need to bring the equation to standard quadratic form $ax^2 + bx + c = 0$ by combining like terms. $\newline$ $-7x^2 + 54x - 231 = -4x^2$ $\newline$ Add $4x^2$ to both sides to combine the $x^2$ terms. $\newline$ $(-7x^2 + 4x^2) + 54x - 231 = 0$ $\newline$ $-3x^2 + 54x - 231 = 0$
Identify Coefficients: Now that we have the quadratic equation in standard form, we can identify the coefficients $a$ , $b$ , and $c$ . $a = -3$ , $b = 54$ , $c = -231$
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. $D = 54^2 - 4(-3)(-231)$
Find Value: Perform the calculations to find the value of the discriminant. $\newline$ $D = 2916 - 4(3)(231)$ $\newline$ $D = 2916 - 2772$ $\newline$ $D = 144$

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