For the following quadratic equation, find the discriminant. 3x^(2)+42 x+74=6x-7 Answer:

Rearrange equation: Bring all terms to one side of the equation to get it into standard quadratic form ax^2 + bx + c = 0. 3x^2 + 42x + 74 - 6x + 7 = 0 Combine like terms. 3x^2 + (42x - 6x) + (74 + 7) = 0 3x^2 + 36x + 81 = 0Identify coefficients: Identify the coefficients a, b, and c from the standard form of the quadratic equation. a = 3, b = 36, c = 81Use discriminant formula: Use the discriminant formula for a quadratic equation, which is b^2 - 4ac. Discriminant (D) = b^2 - 4acSubstitute values: Substitute the identified values into the discriminant formula. D = 36^2 - 4(3)(81)Calculate discriminant: Calculate the discriminant. D = 1296 - 4(3)(81) D = 1296 - 972 D = 324

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For the following quadratic equation, find the discriminant.

3x^(2)+42 x+74=6x-7
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $3 x^{2}+42 x+74=6 x-7$ $\newline$ Answer:

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Algebra 2

Solve exponential equations by rewriting the base

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

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3 x^{2}+42 x+74=6 x-7

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Answer:

Rearrange equation: Bring all terms to one side of the equation to get it into standard quadratic form $ax^2 + bx + c = 0$ .
$3x^2 + 42x + 74 - 6x + 7 = 0$
Combine like terms.
$3x^2 + (42x - 6x) + (74 + 7) = 0$
$3x^2 + 36x + 81 = 0$
Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation. $a = 3$ , $b = 36$ , $c = 81$
Use discriminant formula: Use the discriminant formula for a quadratic equation, which is $b^2 - 4ac$ . Discriminant ( $D$ ) = $b^2 - 4ac$
Substitute values: Substitute the identified values into the discriminant formula. $\newline$ $D = 36^2 - 4(3)(81)$
Calculate discriminant: Calculate the discriminant. $\newline$ $D = 1296 - 4(3)(81)$ $\newline$ $D = 1296 - 972$ $\newline$ $D = 324$