What are the values of $a, b$, and $c$ in the quadratic equation $-2 x^2+4 x-3=0$?
A. $a=2, b=4, c=3$
B. $a=2, b=4, c=-3$
C. $a=-2, b=4, c=3$
D. $a=-2, b=4, c=-3

Identify the quadratic equation: − 2 x 2 + 4 x − 3 = 0 .
Compare with the standard form: a x 2 + b x + c = 0 .
Determine the coefficients: a = − 2 , b = 4 , c = − 3 .
The values are: a = − 2 , b = 4 , c = − 3 ​ .

Explanation

Identifying the coefficients We are given the quadratic equation − 2 x 2 + 4 x − 3 = 0 . We need to identify the coefficients a , b , and c in the standard form of a quadratic equation, which is a x 2 + b x + c = 0 .

Determining the values of a, b, and c Comparing the given equation − 2 x 2 + 4 x − 3 = 0 with the standard form a x 2 + b x + c = 0 , we can identify the coefficients as follows:



The coefficient of x 2 is a , so a = − 2 .
The coefficient of x is b , so b = 4 .
The constant term is c , so c = − 3 .


Final Answer Therefore, the values of a , b , and c in the quadratic equation − 2 x 2 + 4 x − 3 = 0 are a = − 2 , b = 4 , and c = − 3 .

Examples
Understanding quadratic equations is crucial in various fields, such as physics and engineering. For example, when analyzing the trajectory of a projectile, the height of the projectile can be modeled using a quadratic equation. The coefficients a , b , and c in the equation determine the shape and position of the trajectory. By correctly identifying these coefficients, we can accurately predict the projectile's path and landing point. This has practical applications in sports, military science, and even weather forecasting.

Answered by GinnyAnswer | 2025-07-03

The coefficients in the quadratic equation − 2 x 2 + 4 x − 3 = 0 are a = − 2 , b = 4 , and c = − 3 . Therefore, the answer is option D.
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Answered by Anonymous | 2025-07-04