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For the following quadratic equation, find the discriminant.

-4x^(2)+18 x+112=2x
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-4 x^{2}+18 x+112=2 x$ $\newline$ Answer:

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Solve exponential equations by rewriting the base

Full solution

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

\newline

-4 x^{2}+18 x+112=2 x

\newline

Answer:

Rewrite in Standard Form: First, we need to rewrite the quadratic equation in standard form, which is $ax^2 + bx + c = 0$ .
$-4x^2 + 18x + 112 = 2x$
Subtract $2x$ from both sides to get:
$-4x^2 + 16x + 112 = 0$
Identify Coefficients: Now that we have the quadratic equation in standard form, we can identify the coefficients $a$ , $b$ , and $c$ . $a = -4$ , $b = 16$ , and $c = 112$
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: $D = (16)^2 - 4(-4)(112)$
Perform Calculations: Now, perform the calculations: $\newline$ $D = 256 - 4(-4)(112)$ $\newline$ $D = 256 + 1792$ $\newline$ $D = 2048$

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