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For the following quadratic equation, find the discriminant.

-11x^(2)+90 x-160=-6x^(2)
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-11 x^{2}+90 x-160=-6 x^{2}$ $\newline$ Answer:

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Transformations of functions

Full solution

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

\newline

-11 x^{2}+90 x-160=-6 x^{2}

\newline

Answer:

Simplify Quadratic Equation: First, we need to simplify the quadratic equation by moving all terms to one side of the equation. $\newline$ $-11x^{2} + 90x - 160 = -6x^{2}$ $\newline$ Add $6x^{2}$ to both sides to combine like terms. $\newline$ $-11x^{2} + 6x^{2} + 90x - 160 = 0$ $\newline$ $-5x^{2} + 90x - 160 = 0$
Find Discriminant: Now that we have the simplified quadratic equation in the form $ax^{2} + bx + c = 0$ , we can find the discriminant using the formula $b^{2} - 4ac$ . For our equation, $a = -5$ , $b = 90$ , and $c = -160$ .
Calculate Discriminant: Calculate the discriminant using the values of $a$ , $b$ , and $c$ . $\newline$ Discriminant ( $D$ ) = $b^{2} - 4ac$ $\newline$ $D = 90^{2} - 4(-5)(-160)$
Perform Calculations: Perform the calculations. $\newline$ $D = 8100 - 4(-5)(-160)$ $\newline$ $D = 8100 - (20)(160)$ $\newline$ $D = 8100 - 3200$
Subtract to Find Value: Subtract $3200$ from $8100$ to find the value of the discriminant. $\newline$ $D = 8100 - 3200$ $\newline$ $D = 4900$

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