For the following quadratic equation, find the discriminant. -4x^(2)+10 x-18=-3x^(2)+7 Answer:

Bring to Standard Form: First, we need to bring the quadratic equation to standard form, which is ax^2 + bx + c = 0. To do this, we will move all terms to one side of the equation by adding 3x^2 to both sides and subtracting 7 from both sides. Calculation: -4x^2 + 10x - 18 + 3x^2 - 7 = 0Simplify the Equation: Now, we simplify the equation by combining like terms. Calculation: (-4x^2 + 3x^2) + 10x + (-18 - 7) = 0 This simplifies to: -x^2 + 10x - 25 = 0Identify Coefficients: Next, we identify the coefficients a, b, and c from the standard form of the quadratic equation, where a is the coefficient of x^2, b is the coefficient of x, and c is the constant term. In our equation, a = -1, b = 10, and c = -25.Calculate Discriminant: The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac. We will use the values of a, b, and c we found in the previous step to calculate the discriminant. Calculation: D = (10)^2 - 4*(-1)*(-25)Find Discriminant: Now, we perform the calculation to find the discriminant. Calculation: D = 100 - 4*1*25 D = 100 - 100 D = 0

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For the following quadratic equation, find the discriminant.

-4x^(2)+10 x-18=-3x^(2)+7
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-4 x^{2}+10 x-18=-3 x^{2}+7$ $\newline$ Answer:

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

\newline

-4 x^{2}+10 x-18=-3 x^{2}+7

\newline

Answer:

Bring to Standard Form: First, we need to bring the quadratic equation to standard form, which is $ax^2 + bx + c = 0$ . To do this, we will move all terms to one side of the equation by adding $3x^2$ to both sides and subtracting $7$ from both sides. $\newline$ Calculation: $-4x^2 + 10x - 18 + 3x^2 - 7 = 0$
Simplify the Equation: Now, we simplify the equation by combining like terms. $\newline$ Calculation: $(-4x^2 + 3x^2) + 10x + (-18 - 7) = 0$ $\newline$ This simplifies to: $-x^2 + 10x - 25 = 0$
Identify Coefficients: Next, we identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation, where $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ , and $c$ is the constant term. $\newline$ In our equation, $a = -1$ , $b = 10$ , and $b$ $0$ .
Calculate Discriminant: The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . We will use the values of $a$ , $b$ , and $c$ we found in the previous step to calculate the discriminant. $\newline$ Calculation: $D = (10)^2 - 4(-1)(-25)$
Find Discriminant: Now, we perform the calculation to find the discriminant. $\newline$ Calculation: $D = 100 - 4 \times 1 \times 25$ $\newline$ $D = 100 - 100$ $\newline$ $D = 0$