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What is the discriminant of the quadratic equation
5x^(2)-8x+9=0 ?

-244
244
116

-116

What is the discriminant of the quadratic equation $5 x^{2}-8 x+9=0$ ? $\newline$ $-244$ $\newline$ $244$ $\newline$ $116$ $\newline$ $-116$

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Transformations of functions

Full solution

Q. What is the discriminant of the quadratic equation

5 x^{2}-8 x+9=0

?

\newline

-244

\newline

244

\newline

116

\newline

-116

Identify coefficients and equation: The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . We need to identify the coefficients $a$ , $b$ , and $c$ from the given equation and substitute them into the formula to find the discriminant.
Given quadratic equation: The given quadratic equation is $5x^2 - 8x + 9 = 0$ . Here, the coefficient $a$ is $5$ , the coefficient $b$ is $-8$ , and the coefficient $c$ is $9$ . We will use these values in the discriminant formula.
Substitute values into formula: Substitute $a = 5$ , $b = -8$ , and $c = 9$ into the discriminant formula $D = b^2 - 4ac$ . This gives us $D = (-8)^2 - 4(5)(9)$ .
Calculate the discriminant: Calculate the discriminant using the values from the previous step: $D = 64 - 4(5)(9)$ . First, calculate the square of $-8$ , which is $64$ , and then calculate $4 \times 5 \times 9$ , which is $180$ .
Subtract to find the value: Subtract $180$ from $64$ to find the discriminant: $D = 64 - 180$ .
Subtract to find the value: Subtract $180$ from $64$ to find the discriminant: $D = 64 - 180$ .Perform the subtraction to get the final value of the discriminant: $D = -116$ .

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