Which statement is true about the quadratic equation $8 x^2-5 x+3=0$?
A. The constant term is 8.
B. The constant term is -5.
C. The leading coefficient is 8.
D. The leading coefficient is -5.
Answer (2)
Identify the leading coefficient as the coefficient of the x 2 term, which is 8.
Identify the constant term as the term without any x variable, which is 3.
Compare the identified values with the given options.
The true statement is: The leading coefficient is 8. T h e l e a d in g coe ff i c i e n t i s 8.
Explanation
Identifying the components We are given the quadratic equation 8 x 2 − 5 x + 3 = 0 . We need to identify the leading coefficient and the constant term to determine which statement is true.
Finding the leading coefficient The leading coefficient is the coefficient of the x 2 term. In this equation, the coefficient of x 2 is 8. Therefore, the leading coefficient is 8.
Finding the constant term The constant term is the term without any x variable. In this equation, the constant term is 3.
Determining the true statement Now, let's check the given statements:
The constant term is 8. (False, the constant term is 3)
The constant term is -5. (False, the constant term is 3)
The leading coefficient is 8. (True)
The leading coefficient is -5. (False, the leading coefficient is 8) Therefore, the true statement is: The leading coefficient is 8.
Examples
Quadratic equations are used in various real-life applications, such as calculating the trajectory of a projectile, designing parabolic mirrors, and determining the optimal dimensions for certain structures. Understanding the coefficients and terms of a quadratic equation helps in analyzing and solving these practical problems. For example, if you are launching a rocket, the quadratic equation can help you determine the launch angle needed to reach a specific target. The leading coefficient and constant term play crucial roles in determining the shape and position of the parabolic trajectory.
The leading coefficient of the quadratic equation 8 x 2 − 5 x + 3 = 0 is 8, while the constant term is 3. The true statement among the options provided is that the leading coefficient is 8. Therefore, the correct answer is option C.
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