Question
\( f(x)=3 x^{2}+24 x+48 \) What is the value of the discriminant of \( f \) ? How many distinct real number zeros does \( f \) have? He
Ask by Ramos Goodwin. in the United States
Feb 26,2025
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Tutor-Verified Answer
Answer
The discriminant is 0, and \( f(x) \) has exactly one distinct real zero.
Solution
The discriminant is calculated as b² - 4ac. Here, a = 3, b = 24, and c = 48:
Discriminant = 24² - 4 × 3 × 48 = 576 - 576 = 0.
A discriminant of 0 means the quadratic has exactly one distinct real zero (a repeated or double root).
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Simplify this solution The Deep Dive
To find the discriminant of the quadratic function \( f(x) = 3x^2 + 24x + 48 \), we use the formula \( D = b^2 - 4ac \). Here, \( a = 3 \), \( b = 24 \), and \( c = 48 \). Plugging in these values, we calculate \( D = 24^2 - 4 \times 3 \times 48 = 576 - 576 = 0 \). So, the value of the discriminant is 0. A discriminant of 0 means that the quadratic has exactly one distinct real number zero (or root). This root is referred to as a repeated root, indicating that the graph of the function touches the x-axis at exactly one point.
