For the following quadratic equation, find the discriminant. -6x^(2)-18 x+102=-7x^(2)+2x+2 Answer:

Simplify Equation: First, we need to simplify the given quadratic equation by combining like terms on both sides. The given equation is: -6x^(2) - 18x + 102 = -7x^(2) + 2x + 2Move Terms to One Side: Now, we will move all terms to one side to set the equation to zero. Add 7x^(2) to both sides: -6x^(2) + 7x^(2) - 18x + 102 = 2x + 2 This simplifies to: x^(2) - 18x + 102 = 2x + 2Standard Form: Next, we subtract 2x from both sides and subtract 2 from both sides to get the quadratic equation in standard form: x^(2) - 18x - 2x + 102 - 2 = 0 This simplifies to: x^(2) - 20x + 100 = 0Find Discriminant: Now that we have the quadratic equation in standard form, we can find the discriminant. The discriminant of a quadratic equation ax^(2) + bx + c = 0 is given by the formula: Discriminant (D) = b^(2) - 4acCalculate Discriminant: For our equation x^(2) - 20x + 100 = 0, the coefficients are: a = 1, b = -20, and c = 100 Let's plug these values into the discriminant formula: D = (-20)^(2) - 4(1)(100)Calculate the discriminant: D = 400 - 400 D = 0

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For the following quadratic equation, find the discriminant.

-6x^(2)-18 x+102=-7x^(2)+2x+2
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-6 x^{2}-18 x+102=-7 x^{2}+2 x+2$ $\newline$ Answer:

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

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-6 x^{2}-18 x+102=-7 x^{2}+2 x+2

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Answer:

Simplify Equation: First, we need to simplify the given quadratic equation by combining like terms on both sides. $\newline$ The given equation is: $\newline$ $-6x^{2} - 18x + 102 = -7x^{2} + 2x + 2$
Move Terms to One Side: Now, we will move all terms to one side to set the equation to zero. $\newline$ Add $7x^{2}$ to both sides: $\newline$ $-6x^{2} + 7x^{2} - 18x + 102 = 2x + 2$ $\newline$ This simplifies to: $\newline$ $x^{2} - 18x + 102 = 2x + 2$
Standard Form: Next, we subtract $2x$ from both sides and subtract $2$ from both sides to get the quadratic equation in standard form: $\newline$ $x^{2} - 18x - 2x + 102 - 2 = 0$ $\newline$ This simplifies to: $\newline$ $x^{2} - 20x + 100 = 0$
Find Discriminant: Now that we have the quadratic equation in standard form, we can find the discriminant. The discriminant of a quadratic equation $ax^{2} + bx + c = 0$ is given by the formula: $\newline$ Discriminant $(D) = b^{2} - 4ac$
Calculate Discriminant: For our equation $x^{2} - 20x + 100 = 0$ , the coefficients are: $\newline$ $a = 1$ , $b = -20$ , and $c = 100$ $\newline$ Let's plug these values into the discriminant formula: $\newline$ $D = (-20)^{2} - 4(1)(100)$
Calculate Discriminant: For our equation $x^2 - 20x + 100 = 0$ , the coefficients are: $\newline$ a = $1$ , b = $-20$ , and c = $100$ $\newline$ Let's plug these values into the discriminant formula: $\newline$ $D = (-20)^2 - 4(1)(100)$ Calculate the discriminant: $\newline$ $D = 400 - 400$ $\newline$ $D = 0$