For the following quadratic equation, find the discriminant. 5x^(2)-78 x+471=-8x-4 Answer:

Bring to Standard Form: First, we need to bring the equation to standard quadratic form ax^2 + bx + c = 0. We do this by adding 8x and 4 to both sides of the equation. 5x^2 - 78x + 471 + 8x + 4 = 0Combine Like Terms: Now, combine like terms to simplify the equation. 5x^2 - (78x - 8x) + (471 + 4) = 0 5x^2 - 70x + 475 = 0Identify Quadratic Form: The standard form of a quadratic equation is ax^2 + bx + c = 0. In this case, a = 5, b = -70, and c = 475. The discriminant of a quadratic equation is given by the formula D = b^2 - 4ac.Substitute into Discriminant Formula: Substitute the values of a, b, and c into the discriminant formula. D = (-70)^2 - 4(5)(475)Calculate Discriminant: Calculate the discriminant. D = 4900 - 4(5)(475) D = 4900 - 9500Finalize Calculation: Finish the calculation to find the value of the discriminant. D = -4600

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For the following quadratic equation, find the discriminant.

5x^(2)-78 x+471=-8x-4
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $5 x^{2}-78 x+471=-8 x-4$ $\newline$ Answer:

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

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5 x^{2}-78 x+471=-8 x-4

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Answer:

Bring to Standard Form: First, we need to bring the equation to standard quadratic form $ax^2 + bx + c = 0$ . We do this by adding $8x$ and $4$ to both sides of the equation. $5x^2 - 78x + 471 + 8x + 4 = 0$
Combine Like Terms: Now, combine like terms to simplify the equation. $\newline$ $5x^2 - (78x - 8x) + (471 + 4) = 0$ $\newline$ $5x^2 - 70x + 475 = 0$
Identify Quadratic Form: The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . In this case, $a = 5$ , $b = -70$ , and $c = 475$ . The discriminant of a quadratic equation is given by the formula $D = b^2 - 4ac$ .
Substitute into Discriminant Formula: Substitute the values of $a$ , $b$ , and $c$ into the discriminant formula. $D = (-70)^2 - 4(5)(475)$
Calculate Discriminant: Calculate the discriminant. $\newline$ $D = 4900 - 4(5)(475)$ $\newline$ $D = 4900 - 9500$
Finalize Calculation: Finish the calculation to find the value of the discriminant. $D = -4600$