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For the following quadratic equation, find the discriminant.

x^(2)+2x+8=8
Answer:

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

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Solve exponential equations by rewriting the base

Full solution

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

\newline

x^{2}+2 x+8=8

\newline

Answer:

Write Standard Form: Write the quadratic equation in standard form. $\newline$ The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . Subtract $8$ from both sides of the equation to get it into standard form. $\newline$ $x^2 + 2x + 8 - 8 = 0$ $\newline$ $x^2 + 2x = 0$
Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation. $\newline$ From the equation $x^2 + 2x = 0$ , we can see that: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 2$ (coefficient of $x$ ) $\newline$ $c = 0$ (constant term)
Use Discriminant Formula: Use the discriminant formula to find the discriminant of the quadratic equation. $\newline$ The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . $\newline$ Plugging in the values of $a$ , $b$ , and $c$ , we get: $\newline$ $D = (2)^2 - 4(1)(0)$ $\newline$ $D = 4 - 0$ $\newline$ $D = 4$

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f(x) = \frac{1}{6^x}

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