For the following quadratic equation, find the discriminant. x^(2)-16 x+51=4x-2 Answer:

Rephrase the Question: First, let's rephrase the ＂What is the discriminant of the quadratic equation x^2 - 16x + 51 = 4x - 2?＂Standard Form Conversion: To find the discriminant, we need to write the quadratic equation in the standard form ax^2 + bx + c = 0. Let's move all terms to one side of the equation to do this. x^2 - 16x + 51 - (4x - 2) = 0Combine Like Terms: Now, let's simplify the equation by combining like terms. x^2 - 16x + 51 - 4x + 2 = 0 x^2 - 20x + 53 = 0Identify Coefficients: The standard form of a quadratic equation is ax^2 + bx + c = 0. In our equation, a = 1, b = -20, and c = 53.Calculate Discriminant Formula: The discriminant of a quadratic equation is given by the formula D = b^2 - 4ac. Let's calculate the discriminant using the values of a, b, and c we found. D = (-20)^2 - 4(1)(53)Perform Calculations: Now, let's perform the calculations. D = 400 - 4(53) D = 400 - 212Find Discriminant Value: Finally, let's subtract 212 from 400 to find the value of the discriminant. D = 188

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For the following quadratic equation, find the discriminant.

x^(2)-16 x+51=4x-2
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $x^{2}-16 x+51=4 x-2$ $\newline$ Answer:

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

\newline

x^{2}-16 x+51=4 x-2

\newline

Answer:

Rephrase the Question: First, let's rephrase the ＂What is the discriminant of the quadratic equation $x^2 - 16x + 51 = 4x - 2$ ?＂
Standard Form Conversion: To find the discriminant, we need to write the quadratic equation in the standard form $ax^2 + bx + c = 0$ . Let's move all terms to one side of the equation to do this. $\newline$ $x^2 - 16x + 51 - (4x - 2) = 0$
Combine Like Terms: Now, let's simplify the equation by combining like terms. $x^2 - 16x + 51 - 4x + 2 = 0$ $x^2 - 20x + 53 = 0$
Identify Coefficients: The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . In our equation, $a = 1$ , $b = -20$ , and $c = 53$ .
Calculate Discriminant Formula: The discriminant of a quadratic equation is given by the formula $D = b^2 - 4ac$ . Let's calculate the discriminant using the values of $a$ , $b$ , and $c$ we found. $\newline$ $D = (-20)^2 - 4(1)(53)$
Perform Calculations: Now, let's perform the calculations. $\newline$ $D = 400 - 4(53)$ $\newline$ $D = 400 - 212$
Find Discriminant Value: Finally, let's subtract $212$ from $400$ to find the value of the discriminant. $\newline$ $D = 188$