For the following quadratic equation, find the discriminant. -x^(2)+4x+11=8x-1 Answer:

Rearrange equation: Bring all terms to one side of the equation to get it into standard quadratic form ax^2 + bx + c = 0. We start by subtracting 8x and adding 1 to both sides of the equation. -x^2 + 4x + 11 - 8x + 1 = 8x - 1 - 8x + 1 This simplifies to: -x^2 - 4x + 12 = 0Identify coefficients: Identify the coefficients a, b, and c in the standard quadratic form. From the equation -x^2 - 4x + 12 = 0, we can see that: a = -1, b = -4, and c = 12Calculate discriminant: Use the discriminant formula to find the discriminant of the quadratic equation. The discriminant D is given by D = b^2 - 4ac. Plugging in the values of a, b, and c, we get: D = (-4)^2 - 4(-1)(12)Calculate the discriminant. D = 16 - 4(-1)(12) D = 16 + 48 D = 64

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For the following quadratic equation, find the discriminant.

-x^(2)+4x+11=8x-1
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-x^{2}+4 x+11=8 x-1$ $\newline$ Answer:

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Solve exponential equations by rewriting the base

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

\newline

-x^{2}+4 x+11=8 x-1

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Answer:

Rearrange equation: Bring all terms to one side of the equation to get it into standard quadratic form $ax^2 + bx + c = 0$ . $\newline$ We start by subtracting $8x$ and adding $1$ to both sides of the equation. $\newline$ $-x^2 + 4x + 11 - 8x + 1 = 8x - 1 - 8x + 1$ $\newline$ This simplifies to: $\newline$ $-x^2 - 4x + 12 = 0$
Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the standard quadratic form. $\newline$ From the equation $-x^2 - 4x + 12 = 0$ , we can see that: $\newline$ $a = -1$ , $b = -4$ , and $c = 12$
Calculate discriminant: Use the discriminant formula to find the discriminant of the quadratic equation. $\newline$ The discriminant $D$ is given by $D = b^2 - 4ac$ . $\newline$ Plugging in the values of $a$ , $b$ , and $c$ , we get: $\newline$ $D = (-4)^2 - 4(-1)(12)$
Calculate discriminant: Use the discriminant formula to find the discriminant of the quadratic equation. $\newline$ The discriminant $D$ is given by $D = b^2 - 4ac$ . $\newline$ Plugging in the values of $a$ , $b$ , and $c$ , we get: $\newline$ $D = (-4)^2 - 4(-1)(12)$ Calculate the discriminant. $\newline$ $D = 16 - 4(-1)(12)$ $\newline$ $D = 16 + 48$ $\newline$ $D = 64$